SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Solving Problems, SM-Bank 016

In the diagram below, find the value of \(a^{\circ}\), giving reasons for your answer.   (2 marks)
  

Show Answers Only

\(46^{\circ}\)

Show Worked Solution

\(\text{Since cointerior angles sum to 180°:}\)

\(180^{\circ}\) \(=a+60+74\)  
\(a^{\circ}\) \(=180-134\)  
  \(=46^{\circ}\)  

Solving Problems, SM-Bank 015

In the diagram below, find the value of \(x^{\circ}\), giving reasons for your answer.   (2 marks)
  

Show Answers Only

\(45^{\circ}\)

Show Worked Solution

\(\text{Since cointerior angles sum to 180°:}\)

\(180^{\circ}\) \(=x+70+65\)  
\(x^{\circ}\) \(=180-135\)  
  \(=45^{\circ}\)  

Solving Problems, SM-Bank 014

In the diagram below, find the value of \(x^{\circ}\), giving reasons for your answer.   (2 marks)
  

Show Answers Only

\(\angle y^{\circ} = 40^{\circ}\ \ \text{(alternate angles)} \)

\(\angle x^{\circ}=360=40 = 320^{\circ}\ \ \text{(360° about a point)}\)

Show Worked Solution

\(\angle y^{\circ} = 40^{\circ}\ \ \text{(alternate angles)} \)

\(\angle x^{\circ}=360=40 = 320^{\circ}\ \ \text{(360° about a point)}\)

Solving Problems, SM-Bank 013

In the diagram below, find the value of \(a^{\circ}\), giving reasons for your answer.   (2 marks)
  

Show Answers Only

\(\angle b^{\circ} = 360-325 = 35^{\circ}\ \ \text{(360° about a point)} \)

\(\angle a^{\circ}=35^{\circ}\ \ \text{(alternate angles)}\)

Show Worked Solution

\(\angle b^{\circ} = 360-325 = 35^{\circ}\ \ \text{(360° about a point)} \)

\(\angle a^{\circ}=35^{\circ}\ \ \text{(alternate angles)}\)

Solving Problems, SM-Bank 012

In the diagram below, find the value of \(x^{\circ}\), giving reasons for your answer.   (2 marks)
  

Show Answers Only

\(\angle y^{\circ} = 180-(52+90) = 38^{\circ}\ \ \text{(180° in straight line)} \)

\(\angle x^{\circ}=38^{\circ}\ \ \text{(alternate angles)}\)

Show Worked Solution

\(\angle y^{\circ} = 180-(52+90) = 38^{\circ}\ \ \text{(180° in straight line)} \)

\(\angle x^{\circ}=38^{\circ}\ \ \text{(alternate angles)}\)

Solving Problems, SM-Bank 011

In the diagram below, \(QR\) is parallel to lines \(SU\) and \(VW\).
 

Find the value of \(x^{\circ}\), giving reasons for your answer.   (3 marks)

Show Answers Only

\(\angle UTQ = 125^{\circ}\ \ \text{(corresponding angles)} \)

\(\angle STX=125^{\circ}\ \ \text{(vertically opposite angles)}\)

\(x^{\circ} = 180-125=55^{\circ} \ \ \text{(cointerior angles)}\)

Show Worked Solution

\(\angle UTQ = 125^{\circ}\ \ \text{(corresponding angles)} \)

\(\angle STX=125^{\circ}\ \ \text{(vertically opposite angles)}\)

\(x^{\circ} = 180-125=55^{\circ} \ \ \text{(cointerior angles)}\)

Solving Problems, SM-Bank 010

In the diagram below, \(BC\) is parallel to \(DE\) and \(\angle ACB\) is a right-angle.
 

Find the value of \(x^{\circ}\), giving reasons for your answer.   (3 marks)

Show Answers Only

\(\text{Extend line}\ BC: \)
 

\(\angle GCF=180-120=60^{\circ}\ \ \text{(180° in a straight line)}\)

\(x^{\circ} = 60^{\circ} \ \ \text{(corresponding angles)}\)

Show Worked Solution

\(\text{Extend line}\ BC: \)
 

\(\angle GCF=180-120=60^{\circ}\ \ \text{(180° in a straight line)}\)

\(x^{\circ} = 60^{\circ} \ \ \text{(corresponding angles)}\)

Solving Problems, SM-Bank 009

In the diagram below, two parallel lines \(OB\) and \(DC\) cut the horizontal transversal \(OE\), and \(OA\) is perpendicular to \(OE\).
 

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

Show Answers Only

\(\angle BOE=90-20=70^{\circ}\ \ \text{(complementary angles)}\)

\(a^{\circ} = 70^{\circ} \ \ \text{(corresponding angles)}\)

Show Worked Solution

\(\angle BOE=90-20=70^{\circ}\ \ \text{(complementary angles)}\)

\(a^{\circ} = 70^{\circ} \ \ \text{(corresponding angles)}\)

Solving Problems, SM-Bank 007

Determine if two lines in the diagram below are parallel, giving reasons for your answer.   (2 marks)
 

Show Answers Only

\(\angle \text{unknown} = 360-310=50^{\circ}\ \ \text{(360° about a point)}\)

\(\text{Since cointerior angles sum to 180°:}\)

\(140 + 50= 190^{\circ} \neq 180^{\circ}\)

\(\therefore \ \text{Lines are not parallel.}\)

Show Worked Solution

\(\angle \text{unknown} = 360-310=50^{\circ}\ \ \text{(360° about a point)}\)

\(\text{Since cointerior angles sum to 180°:}\)

\(140 + 50 = 190^{\circ} \neq 180^{\circ}\)

\(\therefore \ \text{Lines are not parallel.}\)

Solving Problems, SM-Bank 008

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

Show Answers Only

\(40^{\circ}\)

Show Worked Solution

\(\text{Since cointerior angles sum to 180°:}\)

\(180\) \(=x+65+75\)  
\(180\) \(=x+140\)  
\(x^{\circ}\) \(=180-40\)  
  \(=40^{\circ}\)  

Volume, SM-Bank 070

Convert 485 millilitres to litres.  (1 mark)

Show Answers Only

\(0.485\ \text{ L}\)

Show Worked Solution
\(1000\ \text{mL}\) \(=1\ \text{L}\)
\(\therefore\ 485\ \text{mL}\) \(=\Bigg(\dfrac{485}{1000}\Bigg)\text{ L}\)
  \(=0.485\ \text{ L}\)

Volume, SM-Bank 069

Convert 7350 millilitres to litres.  (1 mark)

Show Answers Only

\(7.350\ \text{ L}\)

Show Worked Solution
\(1000\ \text{mL}\) \(=1\ \text{L}\)
\(\therefore\ 7350\ \text{mL}\) \(=\Bigg(\dfrac{7350}{1000}\Bigg)\text{ L}\)
  \(=7.350\ \text{ L}\)

Volume, SM-Bank 068

Convert 60 000 millilitres to litres.  (1 mark)

Show Answers Only

\(60\ \text{L}\)

Show Worked Solution
\(1000\ \text{mL}\) \(=1\ \text{L}\)
\(\therefore\ 60\ 000\ \text{mL}\) \(=\Bigg(\dfrac{60\ 000}{1000}\Bigg)\text{ L}\)
  \(=60\ \text{ L}\)

Volume, SM-Bank 067

A triangular prism has a volume of 680 cubic centimetres and a height of 5 centimetres. What is the cross-sectional area?  (2 marks)

Show Answers Only

\(136\ \text{m}^2\)

Show Worked Solution
\(V\) \(=Ah\)
\(680\) \(=A\times 5\)
\(A\) \(=\dfrac{680}{5}\)
  \(=136\)

 
\(\therefore\ \text{The cross-sectional area is }136\ \text{m}^2.\)

Volume, SM-Bank 066

Gavin is going camping in the summer holidays and purchased the two-person tent shown below.

  1. Given the triangular face of the tent is isosceles, use Pythagoras' Theorem to calculate the perpendicular height of the tent.  (2 marks)
  2. Using your answer from (a), calculate the volume of the tent in cubic metres.  (2 marks)
  3. What is the capacity of the tent in litres?  (1 mark)
Show Answers Only

a.    \(2\ \text{m}\)

b.    \(12 \text{m}^3\)

c.    \(12\ 000\ \text{L}\)

Show Worked Solution
a.    \(a^2+b^2\) \(=c^2\)
  \(x^2+1.5^2\) \(=2.5^2\)
  \(x^2\) \(=2.5^2-1.5^2\)
  \(x^2\) \(=4\)
  \(x\) \(=\sqrt{4}=2\)

 
\(\therefore\ \text{The perpendicular height of the tent is }2\ \text{metres.}\)
 

b.    \(V\) \(=Ah\)
    \(=\Big(\dfrac{1}{2}\times 3\times 2\Big)\times 4\)
    \(=3\times 4\)
    \(=12\ \text{m}^3\)

 

c.    \(1\ \text{m}^3\) \(=1000\ \text{L}\)
  \(\therefore\ 12\ \text{m}^3\) \(=12\ 000\ \text{L}\)

  
\(\therefore\ \text{The capacity of the tent is }12\ 000\ \text{litres.}\)

Volume, SM-Bank 065

  1. Given the triangular face of the prism above is isosceles, use Pythagoras' Theorem to calculate its perpendicular height. Give your answer correct to the nearest whole centimetre.  (2 marks)
  2. Using your answer from (a), calculate the volume of the prism in cubic centimetres.  (2 marks)
Show Answers Only

a.    \(7\ \text{cm}\)

b.    \(168\ \text{cm}^3\)

Show Worked Solution
a.    \(a^2+b^2\) \(=c^2\)
  \(a^2+3^2\) \(=7.6^2\)
  \(a^2\) \(=7.6^2-3^2\)
  \(a^2\) \(=48.76\)
  \(a\) \(=\sqrt{48.76}=6.982\dots\)
  \(a\) \(\approx 7\)

 
\(\therefore\ \text{The perpendicular height of the triangle is }7\ \text{cm, (nearest whole centimetre).}\)
 

b.    \(V\) \(=Ah\)
    \(=\Big(\dfrac{1}{2}\times 6\times 7\Big)\times 8\)
    \(=21\times 8\)
    \(=168\ \text{cm}^3\)

Volume, SM-Bank 064

  1. For the triangular prism above, use Pythagoras' Theorem to calculate the perpendicular height, \(x\), of the triangular face.  (2 marks)
  2. Using your answer from (a), calculate the volume of the prism in cubic millimetres.  (2 marks)
Show Answers Only

a.    \(5\ \text{mm}\)

b.    \(480\ \text{mm}^3\)

Show Worked Solution
a.    \(a^2+b^2\) \(=c^2\)
  \(x^2+12^2\) \(=13^2\)
  \(x^2\) \(=13^2-12^2\)
  \(x^2\) \(=25\)
  \(x\) \(=\sqrt{25}=5\)

 
\(\therefore\ \text{The perpendicular height of the triangle is }5\ \text{mm}\)
 

b.    \(V\) \(=Ah\)
    \(=\Big(\dfrac{1}{2}\times 12\times 5\Big)\times 16\)
    \(=30\times 16\)
    \(=480\ \text{mm}^3\)

Volume, SM-Bank 063

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

Show Answers Only

\(648\ \text{m}^3\)

Show Worked Solution
\(V\) \(=Ah\)
  \(=\Big(\dfrac{1}{2}\times 8\times 9\Big)\times 18\)
  \(=36\times 18\)
  \(=648\ \text{m}^3\)

Volume, SM-Bank 062

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

Show Answers Only

\(102.362\ \text{cm}^3\)

Show Worked Solution
\(V\) \(=Ah\)
  \(=\Big(\dfrac{1}{2}\times 3.1\times 5.2\Big)\times 12.7\)
  \(=8.06\times 12.7\)
  \(=102.362\ \text{cm}^3\)

Volume, SM-Bank 061

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

Show Answers Only

\(105\ \text{m}^3\)

Show Worked Solution
\(V\) \(=Ah\)
  \(=\Big(\dfrac{1}{2}\times 6\times 5\Big)\times 7\)
  \(=15\times 7\)
  \(=105\ \text{m}^3\)

Volume, SM-Bank 060

A children's rectangular swimming pool measures 175 cm × 180 cm × 30 cm.

  1. Find the volume of the swimming pool in cubic centimetres.  (2 marks)

  2. What is the capacity of the swimming pool in litres?  (1 mark)

Show Answers Only

a.    \(945\ 000\ \text{cm}^3\)

b.    \(945\ \text{L}\)

Show Worked Solution
a.     \(V\) \(=Ah\)  
    \(=(175\times 180)\times 30\)
    \(=945\ 000\ \text{cm}^3\)

 
b.    \(1\ \text{L}=1000\ \text{cm}^3\)

\(945\ 000\ \text{cm}^3\) \(=\Bigg(\dfrac{945\ 000}{1000}\Bigg)\ \text{L}\)
  \(=945\ \text{L}\)

 
\(\therefore\ \text{The swimming pool will hold 945 litres of water.}\)

Volume, SM-Bank 059

During the construction of a new house a concrete slab in the shape of a rectangular prism is to be poured.

The slab measures 20 m × 15 m × 0.15 m.

  1. Find the volume of the concrete required for the slab in cubic metres.  (2 marks)

  2. Calculate the cost of the concrete if it costs $350 per cubic metre.  (2 marks)

Show Answers Only

a.    \(45\ \text{m}^3\)

b.    \($15\ 750\)

Show Worked Solution
a.     \(V\) \(=Ah\)  
  \(V\) \(=(20\times 15)\times 0.15\)
    \(=45\ \text{m}^3\)

 

b.    \(\text{Cost}\) \(=\text{Price}\times \text{Concrete}\)
    \(=$350\times 45\)
    \(=$15\ 750\)

Volume, SM-Bank 058

A rectangular sand pit measures 150 cm × 200 cm × 45 cm.

  1. Find the volume of the sand pit in cubic centimetres.  (2 marks)

  2. How many cubic metres of sand will the sand pit hold?  (1 mark)

Show Answers Only

a.    \(1\ 350\ 000\ \text{cm}^3\)

b.    \(1.35\ \text{m}^3\)

Show Worked Solution
a.     \(V\) \(=Ah\)  
  \(V\) \(=(150\times 200)\times 45\)
    \(=1\ 350\ 000\ \text{cm}^3\)

 
b.    \(1\ \text{m}=100\ \text{cm}\)

\(\therefore\ 1\ \text{m}^3=(100\times 100\times 100)\ \text{cm}^3\)

\(\therefore\ 1\ 350\ 000\ \text{cm}^3\) \(=\Bigg(\dfrac{1\ 350\ 000}{100\times 100\times 100}\Bigg)\ \text{m}^3\)
  \(=1.35\ \text{m}^3\)

 
\(\therefore\ \text{The sandpit will hold }1.35\ \text{cubic metres of sand.}\)

Volume, SM-Bank 057

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

Show Answers Only

\(104\ 832\ \text{mm}^3\)

Show Worked Solution
\(V\) \(=Ah\)
\(V\) \(=(39\times 42)\times 64\)
  \(=104\ 832\ \text{mm}^3\)

Volume, SM-Bank 056

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

Show Answers Only

\(402.57\ \text{cm}^3\)

Show Worked Solution
\(V\) \(=Ah\)
\(V\) \(=(4.2\times 13.5)\times 7.1\)
  \(=402.57\ \text{cm}^3\)

Volume, SM-Bank 055

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

Show Answers Only

\(360\ \text{m}^3\)

Show Worked Solution
\(V\) \(=Ah\)
\(V\) \(=(5\times 9)\times 8\)
  \(=360\ \text{m}^3\)

Volume, SM-Bank 054

The prism below has a height of 100 metres.

Given its volume is 485 cubic metres, calculate the cross-sectional area, \((A)\), of the prism.  (2 marks)
 

Show Answers Only

\(4.85\ \text{m}^2\)

Show Worked Solution

\(V=485\ \text{m}^3\ \text{and }h=100\ \text{m}\)

\(V\) \(=Ah\)
\(485\) \(=100A\)
\(A\) \(=\dfrac{485}{100}\)
\(A\) \(=4.85\ \text{m}^2\)

Volume, SM-Bank 053

The prism below has a height of 23 centimetres.

Given its volume is 391 cubic centimetres, calculate the cross-sectional area, \((A)\), of the prism.  (2 marks)
 

Show Answers Only

\(17\ \text{cm}^2\)

Show Worked Solution

\(V=391\ \text{cm}^3\ \text{and }h=23\ \text{cm}\)

\(V\) \(=Ah\)
\(391\) \(=23A\)
\(A\) \(=\dfrac{391}{23}\)
\(A\) \(=17\ \text{cm}^2\)

Volume, SM-Bank 052

The prism below has a cross-sectional area of 15 square millimetres.

Given its volume is 184.5 cubic millimetres, calculate the height, \((h)\), of the prism.  (2 marks)
 

Show Answers Only

\(12.3\ \text{mm}\)

Show Worked Solution

\(V=184.5\ \text{mm}^3\ \text{and }A=15\ \text{mm}^2\)

\(V\) \(=Ah\)
\(184.5\) \(=15h\)
\(h\) \(=\dfrac{184.5}{15}\)
\(h\) \(=12.3\ \text{mm}\)

Volume, SM-Bank 051

The prism below has a cross-sectional area of 50 square centimetres.

Its volume is 425 cubic centimetres.
 

Calculate the height, \((h)\), of the prism.  (2 marks)

Show Answers Only

\(8.5\ \text{cm}\)

Show Worked Solution

\(V=425\ \text{cm}^3\ \text{and }A=50\ \text{cm}^2\)

\(V\) \(=Ah\)
\(425\) \(=50h\)
\(h\) \(=\dfrac{425}{50}\)
\(h\) \(=8.5\ \text{cm}\)

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.
 

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

  2. 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)

Show Answers Only

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.
 

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

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

Show Answers Only

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)

Show Answers Only

\(0.64\ \text{m}^3\)

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)

Show Answers Only

\(0.125\ \text{m}^3\)

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)

Show Answers Only

\(1.1\ \text{m}\)

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)

Show Answers Only

\(0.7\ \text{m}\)

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)

Show Answers Only

\(49\ \text{cm}\)

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)

Show Answers Only

\(3\ \text{mm}\)

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)

Show Answers Only

\(9261\ \text{mm}^3\)

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)

Show Answers Only

\(729\ \text{m}^3\)

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)

Show Answers Only

\(46.656\ \text{m}^3\)

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)

Show Answers Only

\(64\ \text{cm}^3\)

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)
  

  

Show Answers Only

\(15.625\ \text{m}^3\)

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)
  

  

Show Answers Only

\(3.375\ \text{mm}^3\)

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)
  

  

Show Answers Only

\(8\ \text{m}^3\)

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)
  

  

Show Answers Only

\(1728\ \text{cm}^3\)

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?

  1. \(7.5\ \text{cm}^3\)
  2. \(37.5\ \text{cm}^3\)
  3. \(75\ \text{cm}^3\)
  4. \(375\ \text{cm}^3\)
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?

  1. \(2.8\ \text{m}^3\)
  2. \(5.6\ \text{m}^3\)
  3. \(0.28\ \text{m}^3\)
  4. \(0.56\ \text{m}^3\)
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?

  1. \($864\)
  2. \($2880\)
  3. \($22\ 600\)
  4. \($86\ 400\)
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)

Show Answers Only

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

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)

Show Answers Only

\(56\ 784\ \text{litres}\)

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)

Show Answers Only

\(2376\ \text{litres}\)

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)

Show Answers Only

\(4500\ \text{litres}\)

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

\(\text{Volume of each prism:}\)

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

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

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

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

\(\Rightarrow A\)