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Volume, SM-Bank 047

A shipping container in the shape of a rectangular prism is being transported by truck to a construction site.

The dimensions of the container are marked on the diagram below and are in metres.

Calculate the volume of the shipping container in cubic metres. (2 marks)

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The shipping container is to be converted into a small lap pool on site.
Calculate the capacity of the lap pool when full, giving your answer in kilolitres? (1 mark)

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a. $8.1\ \text{m}^3$

b. $8.1\ \text{kL}$

Show Worked Solution

a.	$V$	$=Ah$
	$V$	$=1.8\times 1.5\times 3$
		$=8.1\ \text{m}^3$

b. $1\ \text{m}^3=1\ \text{kL}$

$\therefore\ 8.1\ \text{m}^3=8.1\ \text{kL}$

$\therefore\ \text{Capacity of the lap pool when full is }8.1\ \text{kilolitres.}$

Volume, SM-Bank 046

A fish tank is in the shape of a cube with a side length of 20 centimetres.

Calculate the volume of the fish tank in cubic centimetres. (2 marks)

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What is the capacity of the fish tank in litres? (1 mark)

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a. $8000\ \text{cm}^3$

b. $8\ \text{litres}$

Show Worked Solution

a.	$V$	$=Ah$
		$=20\times 20\times 20$
		$=8\ 000\ \text{cm}^3$

b. $1000\ \text{cm}^3=1\ \text{litre}$

$8000\ \text{cm}^3=8\ \text{litres}$

$\therefore\ \text{Capacity of fish tank is }8\ \text{litres.}$

Volume, SM-Bank 045

A packing box is in the shape of a cube with a side length of 40 centimetres.

Calculate the volume of the packing box in cubic metres. (2 marks)

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$0.64\ \text{m}^3$

Show Worked Solution

$\text{Convert measurements to metres before substituting into formula.}$

$100\ \text{cm}=1\ \text{m}$

$\therefore\ 40\ \text{cm}=0.40\ \text{m}$

$\text{Volume}$	$=Ah$
$V$	$=0.40\times 0.40\times 0.40$
	$=0.64\ \text{m}^3$

Volume, SM-Bank 044

A paper recycling bag is in the shape of a cube with a side length of 0.5 metres.

Estimate the volume of the recycling bag in cubic metres. (2 marks)

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$0.125\ \text{m}^3$

Show Worked Solution

$\text{Volume}$	$=Ah$
$V$	$=0.5\times 0.5\times 0.5$
	$=0.125\ \text{m}^3$

Volume, SM-Bank 043

A cooking vat in the shape of a cube has a volume of 1.331 cubic metres.

Calculate the side length of the vat. (2 marks)

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$1.1\ \text{m}$

Show Worked Solution

$\text{Let }s \ \text{be the side length of the cube}$

$\text{Volume}$	$=Ah$
$1.331$	$=s\times s\times s$
$s^3$	$=1.331$
$s$	$=\sqrt[3]{1.331}$
	$=1.1$

$\therefore\ \text{Side length of the vat is 1.1 metres.}$

Volume, SM-Bank 042

Find the side length of a cube with a volume of 0.343 cubic metres. (2 marks)

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$0.7\ \text{m}$

Show Worked Solution

$\text{Let }s \ \text{be the side length of the cube}$

$\text{Volume}$	$=Ah$
$0.343$	$=s\times s\times s$
$s^3$	$=0.343$
$s$	$=\sqrt[3]{0.343}$
	$=0.7$

$\therefore\ \text{Side length of the cube is }0.7\ \text{metres.}$

Volume, SM-Bank 041

Find the side length of a cube with a volume of 117 649 cubic centimetres. (2 marks)

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$49\ \text{cm}$

Show Worked Solution

$\text{Let }s \ \text{be the side length of the cube}$

$\text{Volume}$	$=Ah$
$117\ 649$	$=s\times s\times s$
$s^3$	$=117\ 649$
$s$	$=\sqrt[3]{117\ 649}$
	$=49$

$\therefore\ \text{Side length of the cube is 49 centimetres.}$

Volume SM-Bank 040

Find the side length of a cube with a volume of 27 cubic millimetres. (2 marks)

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$3\ \text{mm}$

Show Worked Solution

$\text{Let }s \ \text{be the side length of the cube}$

$\text{Volume}$	$=Ah$
$27$	$=s\times s\times s$
$s^3$	$=27$
$s$	$=\sqrt[3]{27}$
	$=3$

$\therefore\ \text{Side length of the cube is }3\ \text{millimetres.}$

Volume, SM-Bank 039

Calculate the volume of a cube with a side length of 21 millimetres. (2 marks)

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$9261\ \text{mm}^3$

Show Worked Solution

$\text{Volume}$	$=Ah$
	$=21\times 21\times 21$
	$=9261\ \text{mm}^3$

Volume, SM-Bank 038

Calculate the volume of a cube with a side length of 9 metres. (2 marks)

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$729\ \text{m}^3$

Show Worked Solution

$\text{Volume}$	$=Ah$
	$=9\times 9\times 9$
	$=729\ \text{m}^3$

Volume, SM-Bank 037

Calculate the volume of a cube with a side length of 3.6 metres. (2 marks)

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$46.656\ \text{m}^3$

Show Worked Solution

$\text{Volume}$	$=Ah$
	$=3.6\times 3.6\times 3.6$
	$=46.656\ \text{m}^3$

Volume, SM-Bank 036

Calculate the volume of a cube with a side length of 4 centimetres. (2 marks)

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$64\ \text{cm}^3$

Show Worked Solution

$\text{Volume}$	$=Ah$
	$=4\times 4\times 4$
	$=64\ \text{cm}^3$

Volume, SM-Bank 035

Calculate the volume of the cube below in cubic metres. (2 marks)

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$15.625\ \text{m}^3$

Show Worked Solution

$\text{Volume}$	$=Ah$
	$=2.5\times 2.5\times 2.5$
	$=15.625\ \text{m}^3$

Volume, SM-Bank 034

Calculate the volume of the cube below in cubic millimetres. (2 marks)

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$3.375\ \text{mm}^3$

Show Worked Solution

$\text{Volume}$	$=Ah$
	$=1.5\times 1.5\times 1.5$
	$=3.375\ \text{mm}^3$

Volume, SM-Bank 033

Calculate the volume of the cube below in cubic metres. (2 marks)

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$8\ \text{m}^3$

Show Worked Solution

$\text{Volume}$	$=Ah$
	$=2\times 2\times 2$
	$=8\ \text{m}^3$

Volume, SM-Bank 032

Calculate the volume of the cube below in cubic centimetres. (2 marks)

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$1728\ \text{cm}^3$

Show Worked Solution

$\text{Volume}$	$=Ah$
	$=12\times 12\times 12$
	$=1728\ \text{cm}^3$

Volume, SM-Bank 031 MC

A timber door wedge is pictured below.

The wedge is in the shape of a triangular prism.

What is the volume of the wedge in cubic centimetres?

$7.5\ \text{cm}^3$
$37.5\ \text{cm}^3$
$75\ \text{cm}^3$
$375\ \text{cm}^3$

Show Answers Only

$B$

Show Worked Solution

$\text{10 mm =1 cm}$

$\text{Volume}$	$=Ah$
	$=\bigg(\dfrac{1}{2}\times 10\times 3\bigg)\times 2.5$
	$=15\times 2.5$
	$=37.5\ \text{cm}^3$

$\Rightarrow\ B$

Volume, SM-Bank 030 MC

A wheelchair ramp is pictured below.

The ramp is in the shape of a triangular prism.

What is the volume of the ramp?

$2.8\ \text{m}^3$
$5.6\ \text{m}^3$
$0.28\ \text{m}^3$
$0.56\ \text{m}^3$

Show Answers Only

$A$

Show Worked Solution

$\text{Volume}$	$=Ah$
	$=(\dfrac{1}{2}\times 7\times 0.4)\times 2$
	$=1.4\times 2$
	$=2.8\ \text{m}^3$

$\Rightarrow\ A$

Volume, SM-Bank 029 MC

Concrete is poured to make a pathway.

The dimensions of the slab are shown in the diagram below.

If the concrete costs $180 per cubic metre to pour, what is the cost of pouring the slab?

$$864$
$$2880$
$$22\ 600$
$$86\ 400$

Show Answers Only

$A$

Show Worked Solution

$30\ \text{cm}=0.3\ \text{m}$

$\text{Volume of slab}$	$=8\times 0.3\times 2$
	$=4.8\ \text{m}^3$

$\text{Cost of pouring slab}$	$=4.8\times $180$
	$=$864$

$\Rightarrow\ A$

Volume, SM-Bank 028

A kitchen sink is in the shape of a rectangular prism.

Its measurements can be seen below:

If one cubic metre holds 1000 litres of water, how many litres of water will it take to fill the kitchen sink?

Give your answer correct to the nearest litre. (2 marks)

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$38\ \text{litres (nearest L)}$

Show Worked Solution

$\text{Volume of kitchen sink}$	$=0.44\times 0.36\times 0.24$
	$=0.038\ 016\ \text{m}^3$

$\text{Capacity of kitchen sink}$	$=0.038\ 016\times 1000$
	$=38.016$
	$\approx 38\ \text{litres (nearest L)}$

Volume, SM-Bank 027

A shipping container in the shape of a rectangular prism is to be converted into a swimming pool.

Its measurements can be seen below:

If one cubic metre holds 1000 litres of water, how many litres of water will the shipping container hold? (2 marks)

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$56\ 784\ \text{litres}$

Show Worked Solution

$\text{Volume of shipping container}$	$=2.4\times 2.6\times 9.1$
	$=56.784\ \text{m}^3$

$\text{Capacity of shipping container}$	$=56.784\times 1000$
	$=56\ 784\ \text{litres}$

Volume, SM-Bank 026

A water trough is in the shape of a rectangular prism.

Its measurements can be seen below:

If one cubic metre holds 1000 litres of water, how many litres of water will the water trough hold? (2 marks)

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$2376\ \text{litres}$

Show Worked Solution

$\text{Volume of water trough}$	$=0.9\times 1.1\times 2.4$
	$=2.376\ \text{m}^3$

$\text{Capacity of water trough}$	$=2.376\times 1000$
	$=2376\ \text{litres}$

Volume, SM-Bank 025

A dog bath is in the shape of a rectangular prism.

Its measurements can be seen below:

If one cubic metre holds 1000 litres of water, how many litres of water will the dog bath hold? (2 marks)

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$4500\ \text{litres}$

Show Worked Solution

$\text{Volume of dog bath}$	$=1.5\times 0.75\times 4$
	$=4.5\ \text{m}^3$

$\text{Capacity of dog bath}$	$=4.5\times 1000$
	$=4500\ \text{litres}$

Volume, SM-Bank 024 MC

The measurements of the prisms below are all in centimetres.

Which prism has the capacity to hold exactly 2 litres of water?

A.	B.

C.	D.

Show Answers Only

$D$

Show Worked Solution

$1\ \text{cm}^3=1\ \text{mL}\ \ \Longrightarrow\ 1000\ \text{cm}^3=1000\ \text{mL}=1\ \text{L}$

$\text{Option A:}=50\times 10\times 40=20\ 000\ \text{cm}^3\ \Longrightarrow 20\ \text{L}$

$\text{Option B:}=20\times 100\times 50=100\ 000\ \text{cm}^3\ \Longrightarrow 100\ \text{L}$

$\text{Option C:}=200\times 200\times 200=8\ 000\ 000\ \text{cm}^3\ \Longrightarrow 8000\ \text{L}$

$\text{Option D:}=10\times 10\times 20=2000\ \text{cm}^3\ \Longrightarrow 2\ \text{L}\ \checkmark$

$\Rightarrow D$

Volume, SM-Bank 023 MC

The measurements of the prisms below are all in centimetres.

Which prism has the capacity to hold exactly 1 litre of water?

A.	B.

C.	D.

Show Answers Only

$A$

Show Worked Solution

$1\ \text{cm}^3=1\ \text{mL}\ \ \Longrightarrow\ 1000\ \text{cm}^3=1000\ \text{mL}=1\ \text{L}$

$\text{Option A:}=10\times 20\times 5=1000\ \text{cm}^3\ \Longrightarrow 1\ \text{L}\ \checkmark$

$\text{Option B:}=40\times 25\times 10=10\ 000\ \text{cm}^3\ \Longrightarrow 10\ \text{L}$

$\text{Option C:}=40\times 40\times 20=32\ 000\ \text{cm}^3\ \Longrightarrow 32\ \text{L}$

$\text{Option D:}=20\times 10\times 15=3000\ \text{cm}^3\ \Longrightarrow 3\ \text{L}$

$\Rightarrow A$

Volume, SM-Bank 022 MC

Linda made these solid prisms out of identical cubes.

Which prism has the largest volume?

A.	B.

C.	D.

Show Answers Only

$C$

Show Worked Solution

$\text{Volume of each prism:}$

$\text{Option A:}\ \ 8\times 2\times 2=32\ \text{cubes}$

$\text{Option B:}\ \ 3\times 3\times 3=27\ \text{cubes}$

$\text{Option C:}\ \ 6\times 2\times 3=36\ \text{cubes}\ \checkmark$

$\text{Option D:}\ \ 4\times 4\times 2=32\ \text{cubes}$

$\Rightarrow C$

Volume, SM-Bank 021 MC

Armon made these solid prisms out of identical cubes.

Which prism has the largest volume?

A.	B.

C.	D.

Show Answers Only

$A$

Show Worked Solution

$\text{Volume of each prism:}$

$\text{Option A:}\ \ 5\times 2\times 3=30\ \text{cubes}\ \checkmark$

$\text{Option B:}\ \ 7\times 1\times 4=28\ \text{cubes}$

$\text{Option C:}\ \ 7\times 2\times 2=28\ \text{cubes}$

$\text{Option D:}\ \ 3\times 3\times 3=27\ \text{cubes}$

$\Rightarrow A$

Volume, SM-Bank 020 MC

The shaded triangle has an area of 40 cm$^2$

What is the volume of the triangular prism?

$60\ \text{cm}^3$
$120\ \text{cm}^3$
$163\ \text{cm}^3$
$240\ \text{cm}^3$

Show Answers Only

$B$

Show Worked Solution

$V$	$=Ah$
	$=40\times 3$
	$=120\ \text{cm}^3$

$\Rightarrow B$

Volume, SM-Bank 019 MC

The shaded triangle has an area of 80 cm$^2$

What is the volume of the triangular prism?

$800\ \text{cm}^3$
$400\ \text{cm}^3$
$170\ \text{cm}^3$
$165\ \text{cm}^3$

Show Answers Only

$B$

Show Worked Solution

$V$	$=Ah$
	$=80\times 5$
	$=400\ \text{cm}^3$

$\Rightarrow B$

Volume, SM-Bank 018 MC

The shaded rectangle has an area of 60 cm$^2$

What is the volume of the rectangular prism?

$124\ \text{cm}^3$
$128\ \text{cm}^3$
$240\ \text{cm}^3$
$480\ \text{cm}^3$

Show Answers Only

$C$

Show Worked Solution

$V$	$=Ah$
	$=60\times 4$
	$=240\ \text{cm}^3$

$\Rightarrow C$

Volume, SM-Bank 017 MC

The shaded rectangle has an area of 25 cm$^2$

What is the volume of the rectangular prism?

$58\ \text{cm}^3$
$66\ \text{cm}^3$
$200\ \text{cm}^3$
$400\ \text{cm}^3$

Show Answers Only

$C$

Show Worked Solution

$V$	$=Ah$
	$=25\times 8$
	$=200\ \text{cm}^3$

$\Rightarrow C$

Volume, SM-Bank 016

A concrete staircase leading up to the grandstand has 10 steps.

The staircase is 1.6 m high and 3.0 m deep.

Its cross-section comprises identical rectangles.

One of these rectangles is shaded in the diagram below.

Find the area of the shaded rectangle in square metres. (2 marks)

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The concrete staircase is 2.5 m wide.

Find the volume of the solid concrete staircase in cubic metres. (2 marks)

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a. $0.048\ \text{m}^2$

b. $6.6\ \text{m}^3$

Show Worked Solution

a. $\text{Height of rectangle}$

$=\dfrac{1.6}{10}$

$=0.16\ \text{m}$

$\text{Length of rectangle}$

$=\dfrac{3.0}{10}$

$= 0.3\ \text{m}$

$\therefore\ \text{Area of rectangle}$	$=0.16\times 0.3$
	$=0.048\ \text{m}^2$

b. $\text{55 rectangles make up the cross-section}:$

$\therefore\ A$	$=55\times 0.048$
	$= 2.64\ \text{m}^2$

$\therefore\ V$	$=Ah$
	$=2.64\times 2.5$
	$=6.6\ \text{m}^3$

Volume, SM-Bank 015

Khaleda manufactures a face cream. The cream comes in a cylindrical container.

The area of the circular base is 43 cm². The container has a height of 7 cm, as shown in the diagram below.

What is the volume of the container in cubic centimetre? (2 marks)

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$301\ \text{cm}^3$

Show Worked Solution

$V$	$=\text{Area of base}\times \text{height}$
	$=43\times 7$
	$=301\ \text{cm}^3$

Volume, SM-Bank 014

A closed cylindrical water tank has external diameter 3.5 metres.

The external height of the tank is 2.4 metres.

The walls, floor and top of the tank are made of concrete 0.25 m thick.

What is the internal radius, $r$, of the tank? (1 mark)

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What is the internal height, $h$, of the tank? (1 mark)

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Determine the maximum amount of water this tank can hold.
Write your answer correct to the nearest cubic metre. (2 marks)

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a. $1.5\ \text{m}$

b. $13\ \text{m}^3\ \text{(nearest m³)}$

Show Worked Solution

a. $\text{Internal radius}\ (r)$

$=\dfrac{1}{2}\times (3.5-2\times 0.25)$

$=1.5\ \text{m}$

b.	$\text{Internal Height}\ (h)$	$=2.4-(2\times 0.25)$
		$=1.9\ \text{m}$

c.	$\text{Volume}$	$=\pi r^2 h$
		$=\pi\times 1.5^2\times 1.9$
		$=13.430\dots$
		$=13\ \text{m}^3\ \text{(nearest m³)}$

Volume, SM-Bank 013

Miki is planning a gap year in Japan.

She will store some of her belongings in a small storage box while she is away.

This small storage box is in the shape of a rectangular prism.

The diagram below shows that the dimensions of the small storage box are 40 cm × 19 cm × 32 cm.

Calculate the volume of the storage box in cubic centimetres. (2 marks)

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$24320\ \text{cm}^3$

Show Worked Solution

$V$	$=Ah$
	$=32\times 40\times 19$
	$=24320\ \text{cm}^3$

Volume, SM-Bank 012

Tennis balls are packaged in cylindrical containers.

Frank purchases a container of tennis balls that holds three standard tennis balls, stacked one on top of the other.

This container has a radius of 3.4 cm and a height of 20.4 cm, as shown in the diagram below.

Calculate the volume of the cylinder in cubic centimetres, correct to one decimal place. (2 marks)

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If one tennis ball has a volume of 164.6 cm³, how much unused volume, in cubic centimetres, surrounds the tennis balls in this container?
Round your answer to the nearest whole number. (1 mark)

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a. $740.9\ \text{cm}^3\ \text{(to 1 d.p.)}$

b. $247\ \text{cm}^3\ \text{(nearest cm}^3 \text{)}$

Show Worked Solution

a.	$\text{Volume}$	$=Ah$
		$=\pi\times 3.4^2\times 20.4$
		$= 740.86\dots$
		$=740.9\ \text{cm}^3\ \text{(to 1 d.p.)}$

b.	$\text{Unused volume}$	$=\text{cylinder volume}-\text{volume of balls}$
		$= 740.9-3\times 164.6$
		$= 247.1$
		$=247\ \text{cm}^3\ \text{(nearest cm}^3 text{)}$

Volume, SM-Bank 011

The floor of a chicken coop is in the shape of a trapezium.

The floor, $ABCD$, and the chicken coop are shown below.

In the diagram $AB = 3\ \text{m}, BC = 2\ \text{m and}\ \ CD = 5\ \text{m}.$

What is the area of the floor of the chicken coop?

Write your answer in square metres. (2 marks)

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If the height of the chicken coop is 2.4 metres, calculate the volume in cubic metres. (1 mark)

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a. $8\ \text{m}^2$

b. $19.2\ \text{m}^3$

Show Worked Solution

a.	$A$	$=\dfrac{h}{2}(a+b)$
		$=\dfrac{2}{2}(3+5)$
		$= 8\ \text{m}^2$

b.	$V$	$=Ah$
		$=8\times 2.4$
		$=19.2\ \text{m}^3$

Volume, SM-Bank 010

A rectangular block of land has width 50 metres and length 85 metres.

In order to build a house, the builders dig a hole in the block of land.

The hole has the shape of a right-triangular prism, $ABCDEF$.

The width $AD$ = 20 m, length $DC$ = 25 m and height $EC$ = 4 m are shown in the diagram below.

Calculate the volume of the right-triangular prism, $ABCDEF$, giving your answer in cubic metres. (2 marks)

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$1000\ \text{m}^3$

Show Worked Solution

$\text{Cross-section is a triangle}$

$A$	$=\dfrac{1}{2}\times bh$
	$=\dfrac{1}{2}\times 25\times 4$
	$= 50\ \text{m}^2$

$\therefore\ V$	$=50\times 20$
	$=1000\ \text{m}^3$

Volume, SM-Bank 009

A shed has the shape of a prism. Its front face, $AOBCD$, is shaded in the diagram below.

$ABCD$ is a rectangle and $M$ is the midpoint of $AB$.

$\Delta AMO$ is right angled and the length of $AM$ is 3 metres.

Using Pythagoras' Theorem find the length of $OM$. (2 marks)

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Calculate the area of the front face of the shed, $AOBCD$, in square metres. (2 marks)

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Find the volume of the shed in cubic metres. (1 mark)

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a. $1.6\ \text{m}$

b. $18\ \text{m}^2$

c. $180\ \text{m}^3$

Show Worked Solution

$\text{In}\ \Delta AOM,\ \text{using Pythagoras:}$

$OM^2+AM^2$	$=OA^2$
$OM^2+3^2$	$=3.4^2$
$OM^2$	$=3.4^2-3^2$
$OM$	$=\sqrt{3.4^2-3^2}$
	$=\sqrt{2.56}$
	$=1.6\ \text{m}$

b. $\text{Area of front face of shed}$

$=\text{Area}\ \Delta AOB+\text{Area}\ ABCD$

$=\dfrac{1}{2}\times 1.6\times 6+2.2\times 6$

$=18\ \text{m}^2$

c.	$V$	$=Ah$
		$=18\times 10$
		$=180\ \text{m}^3$

Volume, SM-Bank 008

A small cubic box that holds a squash ball has side length of 4.1 centimetres, as shown in the diagram below.

What is the volume, in cubic centimetres, of the box? (2 marks)

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$68.921\ \text{cm}^3$

Show Worked Solution

$\text{Volume}$	$=Ah$
	$=(4.1\times 4.1)\times 4.1$
	$=4.1^3$
	$=68.921\ \text{cm}^3$

Volume, SM-Bank 007

A shipping container has a height of 2.6 m, a width of 2.4 m and a length of 6 m, as shown in the diagram below.

What is the volume, in cubic metres, of the shipping container? (2 marks)

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$37.44\ \text{m}^3$

Show Worked Solution

$\text{Volume}$	$=Ah$
	$=(6\times 2.6)\times 2.4$
	$=37.44\ \text{m}^3$

Volume, SM-Bank 006

A tent with semicircular ends is in the shape of a prism. The diameter of the ends is 1.5 m. The tent is 2.5 m long.

Calculate the total volume of the tent in cubic metres, correct to one decimal place. (2 marks)

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$2.2\ \text{m}^3\ \text{(1 d.p.)}$

Show Worked Solution

$\text{Diameter}=1.5\ \text{metres}\ \ \Rightarrow\ \ \ \text{Radius}= \dfrac{1.5}{2} = 0.75\ \text{metres}$

$V$	$=\dfrac{1}{2}\times \pi r^2h$
	$=\dfrac{1}{2}\times \pi\times 0.75^2\times 2.5$
	$=2.2089\dots$
	$\approx 2.2\ \text{m}^3\ \text{(1 d.p.)}$

Volume, SM-Bank 005

A cake is in the shape of a rectangular prism, as shown in the diagram below.

The cake is cut in half to create two equal portions.

The cut is made along the diagonal, as represented by the dotted line.

Calculate the volume, in cubic centimetres, of one portion of the cake. (2 marks)

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$144\ \text{cm}^3$

Show Worked Solution

$V$	$=\dfrac{1}{2}\times A\times h$
	$=\dfrac{1}{2}\times (6\times 6)\times 8$
	$=144\ \text{cm}^3$

Volume, SM-Bank 004 MC

The solid cylindrical rod shown above has a volume of 490.87 cm³. The length is 25.15 cm.

The radius (in cm) of the cross-section of the rod, correct to one decimal place, is

$2.5$
$5.0$
$6.3$
$19.6$

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$A$

Show Worked Solution

$V=\pi r^2h$

$\text{Where length} =h = 25.15\ \text{cm,}\ V=490.87\ \text{cm}^3$

$\therefore\ 490.87$	$=\pi\times r^2\times 25.15$
$r^2$	$=\dfrac{490.87}{\pi\times 25.15}$
	$= 6.2126\dots$
$\therefore\ r$	$= 2.492\dots\ \text{cm}$
	$\approx 2.5\ \text{cm (1 d.p.)}$

$\Rightarrow A$

Volume, SM-Bank 003 MC

A steel beam used for constructing a building has a cross-sectional area of 0.048 m² as shown.

The beam is 12 m long.

In cubic metres, the volume of this steel beam is closest to

$0.576$
$2.5$
$2.63$
$57.6$

Show Answers Only

$A$

Show Worked Solution

$\text{Volume}$	$=A\times h$
	$=0.048\times 12$
	$=0.576\ \text{m}^3$

$\Rightarrow A$

Unit Conversion, SM-Bank 013

The square below has an area of 1 square centimetre.

Complete the unit conversion equation below:

1 cm² = _____ mm × _____ mm = _______ mm² (1 mark)

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A square has an area of 125 square centimetres.
Using the conversion equation, or otherwise, express the area of the rectangle in square millimetres. (1 mark)

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a. $1\ \text{cm}^{2} = 10\ \text{mm}\ \times\ 10\ \text{mm}\ = 100\ \text{mm}^{2} $

b. $12\ 500\ \text{mm}^{2}$

Show Worked Solution

a. $1\ \text{cm}^{2} = 10\ \text{mm}\ \times\ 10\ \text{mm}\ = 100\ \text{mm}^{2} $

b. $125\ \text{cm}^{2}$	$= 125 \times 100\ \text{mm}^{2} $
	$= 12\ 500\ \text{mm}^{2} $

Volume, SM-Bank 002 MC

A right triangular prism has a volume of 320 cm³.

A second right triangular prism is made with the same width, twice the height and three times the length of the prism shown.

The volume of the second prism (in cm³) is

$640$
$960$
$1280$
$1920$

Show Answers Only

$D$

Show Worked Solution

$\text{Volume of existing prism}\ (V)$

$=A\times l$

$=\Bigg(\dfrac{1}{2}\times b\times h\Bigg)\times l$

$=320\ \text{cm}^3$

$\text{Volume of new prism}\ (V_1)$

$=\Bigg(\dfrac{1}{2}\times b\times 2h\Bigg)\times 3l$

$=6\times\dfrac{1}{2}\times b\times h\times l$

$=6\times V$

$=6\times 320$

$=1920 \ \text{cm}^3$

$\Rightarrow D$

Unit Conversion, SM-Bank 012

The Google main campus in California covers an area of 137 500 square metres.

Using the conversion ratio, 1 hectare = 10 000 m², determine the area of the property in hectares. (1 mark)

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$ 13.75\ \text{ha}$

Show Worked Solution

$\text{Area}$	$= \dfrac{137\ 500}{10\ 000}\ \text{ha} $
	$= 13.75\ \text{ha}$

Volume, SM-Bank 001 MC

The building shown in the diagram is 8 m wide and 24 m long.

The side walls are 4 m high.

The peak of the roof is 6 m vertically above the ground.

In cubic metres, the volume of this building is

$384$
$576$
$960$
$1152$

Show Answers Only

$C$

Show Worked Solution

$\text{Area of front of house}$

$=(4\times 8)+\dfrac{1}{2} (8\times 2)$

$=32+8$

$=40\ \text{m}^2$

$V$	$=Ah$
	$=40\times 24$
	$=960\ \text{m}^3$

$\Rightarrow C$

Unit Conversion, SM-Bank 010

A circle is drawn from a city centre with a radius of 800 metres.

Using the conversion ratio, 1 km² = 1 000 000 m², determine the area of the circle in square kilometres, to two decimal places. (2 marks)

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$ 2.01 \text{km}^{2}$

Show Worked Solution

$\text{Area}$	$= \pi \times 800^{2}\ \text{m}^{2} $
	$= 2\ 010\ 619\ \text{m}^{2}$
	$= \dfrac{2\ 010\ 619}{1\ 000\ 000} $
	$=2.01\ \text{km}^{2} $

Unit Conversion, SM-Bank 009

A Queensland outback pastoralist owns a property with an area of 500 square kilometres.

Using the conversion ratio, 1 km² = 1 000 000 m², determine the exact area of the property in square metres. (2 marks)

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$ 500\ 000\ 000\ \text{m}^{2}$

Show Worked Solution

$\text{Area}$	$= 500 \times 1\ 000\ 000$
	$= 500\ 000\ 000\ \text{m}^{2}$

Unit Conversion, SM-Bank 008

A circle has a radius of 60 centimetres.

Using the conversion ratio, 1 m² = 10 000 cm², or otherwise, calculate the exact area of the circle in square metres. (2 marks)

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$\ 0.36\pi\ \text{m}^{2}$

Show Worked Solution

$\text{Area}$	$= \pi \times 60^{2}$
	$=3600\pi\ \text{cm}^{2}$
	$= \dfrac{3600}{10\ 000}\pi\ \text{m}^{2}$
	$= 0.36\pi\ \text{m}^2 $

Unit Conversion, SM-Bank 007

A poster has an area of 2500 square centimetres.

Using the conversion ratio, 1 m² = 10 000 cm², express this area in square centimetres. (1 mark)

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$0.25\ \text{m}^{2}$

Show Worked Solution

$2500\ \text{cm}^{2}$	$= \dfrac{2500}{10\ 000}\ \text{m}^2$
	$=0.25\ \text{m}^{2}$

Unit Conversion, SM-Bank 006

Athletes throw shot puts from a shot put circle with a standard diameter of 2.13 metres.

Using the conversion ratio, 1 m² = 10 000 cm², or otherwise, calculate the area of a shot put circle to the nearest square centimetres. (3 marks)

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$8\ \text{cm}^{2}$

Show Worked Solution

$\text{Radius}\ = \dfrac{2.13}{2} = 1.065\ \text{m}$

$\text{Area}$	$= \pi \times 1.065^{2}$
	$=3.56327… \text{m}^{2}$
	$=3.56327… \times 10\ 000\ \text{cm}^{2}$
	$=35\ 633\ \text{cm}^2\ \ (\text{nearest cm}^2) $

Unit Conversion, SM-Bank 005

A pickleball court has an area of 81.74 square metres.

Using the conversion ratio, 1 m² = 10 000 cm², express this area in square centimetres. (1 mark)

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$817\ 400\ \text{cm}^{2}$

Show Worked Solution

$81.74\ \text{m}^{2}$	$= 81.74 \times 10\ 000\ \text{cm}^2$
	$=817\ 400\ \text{cm}^{2}$

Unit Conversion, SM-Bank 004

The end of a cylinder has an area of 60 square millimetres.

Using the conversion ratio, 1 cm² = 100 mm², express this area in square centimetres. (1 mark)

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$0.6\ \text{cm}^{2}$

Show Worked Solution

$60\ \text{mm}^{2}$	$= \dfrac{60}{100}\ \text{cm}^2$
	$=0.6\ \text{cm}^{2}$

Unit Conversion, SM-Bank 003

One side of an Australian 10-cent coin has an area of 437 square millimetres.

Using the conversion ratio, 1 cm² = 100 mm², express this area in square centimetres. (1 mark)

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$4.37\ \text{cm}^{2}$

Show Worked Solution

$437\ \text{mm}^{2}$	$= \dfrac{437}{100}\ \text{cm}^2$
	$=4.37\ \text{cm}^{2}$

Unit Conversion, SM-Bank 002

A circle with radius 1 cm, has an area of $\pi$ square centimetres.

Using the conversion ratio, 1 cm² = 100 mm², express the area of the circle in square millimetres. (1 mark)

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$100\pi\ \text{mm}^{2}$

Show Worked Solution

$\pi\ \text{cm}^{2}$	$= \pi \times 100\ \text{mm}^2$
	$=100\pi\ \text{mm}^{2}$

Unit Conversion, SM-Bank 001

A rectangle has an area of 450 square centimetres.

Using the conversion ratio, 1 cm² = 100 mm², express the area of the rectangle in square millimetres. (1 mark)

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$45\ 000\ \text{mm}^{2}$

Show Worked Solution

$450\ \text{cm}^{2}$	$= 450 \times 100\ \text{mm}^{2} $
	$= 45\ 000\ \text{mm}^{2} $

Solving Problems, SM-Bank 028

Find the value of $x^{\circ}$ in the diagram, giving reasons for your answer. (2 marks)

Show Answers Only

$14°$

Show Worked Solution

$\angle RQT + \angle UTQ$	$=180\ \ \text{(cointerior angles)}$
$110+5x$	$=180$
$5x$	$=180-110$
$x^{\circ}$	$=\dfrac{70}{5}$
	$=14^{\circ}$

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a.	\(V\)	\(=Ah\)
	\(V\)	\(=1.8\times 1.5\times 3\)
		\(=8.1\ \text{m}^3\)

a.	\(V\)	\(=Ah\)
		\(=20\times 20\times 20\)
		\(=8\ 000\ \text{cm}^3\)

\(\text{Volume}\)	\(=Ah\)
\(V\)	\(=0.40\times 0.40\times 0.40\)
	\(=0.64\ \text{m}^3\)

\(\text{Volume}\)	\(=Ah\)
\(V\)	\(=0.5\times 0.5\times 0.5\)
	\(=0.125\ \text{m}^3\)

\(\text{Volume}\)	\(=Ah\)
\(1.331\)	\(=s\times s\times s\)
\(s^3\)	\(=1.331\)
\(s\)	\(=\sqrt[3]{1.331}\)
	\(=1.1\)

\(\text{Volume}\)	\(=Ah\)
\(117\ 649\)	\(=s\times s\times s\)
\(s^3\)	\(=117\ 649\)
\(s\)	\(=\sqrt[3]{117\ 649}\)
	\(=49\)

\(\text{Volume}\)	\(=Ah\)
	\(=21\times 21\times 21\)
	\(=9261\ \text{mm}^3\)

\(\text{Volume}\)	\(=Ah\)
	\(=1.5\times 1.5\times 1.5\)
	\(=3.375\ \text{mm}^3\)

\(\text{Volume}\)	\(=Ah\)
	\(=\bigg(\dfrac{1}{2}\times 10\times 3\bigg)\times 2.5\)
	\(=15\times 2.5\)
	\(=37.5\ \text{cm}^3\)