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Volume, SM-Bank 147

A concrete half-pipe was constructed in a park. The pipe has a constant thickness 0.5 metres.
 

  1. Calculate the volume of the concrete used to create the half-pipe, giving your answer to the nearest cubic metre.  (2 marks)
  2. Calculate the capacity of the concrete used in kilolitres.  (1 mark)
Show Answers Only

a.    \(19\ \text{m}^3\)

b.    \(9\ \text{kL}\)

Show Worked Solution

a.    \(\text{diameter large semi-circle = 4 m }\rightarrow\ \text{R = 2 m}\)

\(\text{diameter small semi-circle = 3 m }\rightarrow\ \text{r = 1.5 m}\)

\(\therefore\ V\) \(=\dfrac{1}{2}\times\pi R^2h-\dfrac{1}{2}\times\pi r^2h\)
  \(=\dfrac{1}{2}\times\pi\times 2^2\times 7-\dfrac{1}{2}\times\pi\times 1.5^2\times 7\)
  \(=19.242\dots\)
  \(\approx 19\ \text{m}^3\ (\text{nearest m}^3)\)

 

b.    \(\text{1 kL = 1 m}^3\)

\(\therefore\ 19\ \text{m}^3\) \(=19\ \text{kL}\)

Volume, SM-Bank 146

Geraldine created a large chocolate mould in the shape of a half cylinder using her 3D printer.
 

  1. Calculate the volume of the mould, giving your answer to the nearest cubic centimetre.  (2 marks)
  2. Calculate the capacity of the mould in litres.  (1 mark)
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a.    \(8310\ \text{cm}^3\)

b.    \(8.31\ \text{L}\)

Show Worked Solution

a.    \(\text{diameter = 23 cm }\rightarrow\ \text{radius = 11.5 cm}\)

\(\therefore\ V\) \(=\dfrac{1}{2}\times \pi r^2h\)
  \(=\dfrac{1}{2}\times \pi\times 11.5^2\times 41\)
  \(=8309.512\dots\)
  \(\approx 8310\ \text{cm}^3\ \text{nearest cm}^3)\)

 

b.    \(\text{1 litre = 1000 cm}^3\)

\(\therefore\ 8310\ \text{cm}^3\) \(=\Bigg(\dfrac{8310}{1000}\Bigg)\ \text{L}\)
  \(=8.31\ \text{L}\)

Volume, SM-Bank 122

Calculate the capacity of the prism below in litres.  (2 marks)

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\(140\ 000\ \text{L}\)

Show Worked Solution
\(V\) \(=A\times h\)
  \(=14\times 10\)
  \(=140\ \text{m}^3\)

 
\(\text{1 m}^3=\text{1000 L}\)

 \(\therefore\ \text{Capacity}\) \(=140\times 1000\ \text{L}\)
  \(=140\ 000\ \text{L}\)

Volume, SM-Bank 121

The prism above is a triangular prism.

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

  2. Calculate the capacity of the prism in litres.  (1 mark)
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a.    \(103.23\ \text{cm}^3\)

b.    \(0.10323\ \text{L}\)

Show Worked Solution

a.    \(\text{Note: Convert mm to cm before calculations}\)

\(\text{Cross-sectional area}(A)\) \(=\dfrac{1}{2}\times b\times h\)
  \(=\dfrac{1}{2}\times 6.2\times 4.5\)
  \(=13.95\ \text{cm}^2\)

 

\(V\) \(=A\times h\)
  \(=13.95\times 7.4\)
  \(=103.23\ \text{cm}^3\)

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

 \(\text{Capacity}\) \(=\dfrac{103.23}{1000}\ \text{L}\)
  \(=0.10323\ \text{L}\)

Volume, SM-Bank 120

The prism above is a rectangular prism.

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

  2. Calculate the capacity of the prism in litres.  (1 mark)
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a.    \(15\ \text{m}^3\)

b.    \(15\ 000\ \text{L}\)

Show Worked Solution

a.    \(\text{Note: Convert cm to m before calculations}\)

\(V\) \(=l\times b\times h\)
  \(=2\times 5\times 1.5\)
  \(=15\ \text{m}^3\)

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

 \(\text{Capacity}\) \(=15\times 1000\ \text{L}\)
  \(=15\ 000\ \text{L}\)

Volume, SM-Bank 095

A horse trough is in the shape of a rectangular prism, pictured below.
 

  1.  What is the volume of the prism in cubic centimetres?  (2 marks)
  2. What is the capacity of the horse trough in litres?  (1 mark)
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a.    \(160\ 000\ \text{cm}^3\)

b.    \(160\ \text{L}\)

Show Worked Solution
a.    \(\text{Volume}\) \(=Ah\)
    \(=(40\times 50)\times 80\)
    \(=160\ 000\ \text{cm}^3\)

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

\(\therefore\ \text{Capacity}\) \(=\dfrac{160\ 000}{1000}\)
  \(=160\ \text{L}\)

Volume, SM-Bank 090

A rectangular trough in a paddock provides water for horses.

Its measurements can be seen below:
  

  1. Calculate the volume of the trough in cubic metres.  (2 marks)
  2. Given that one cubic metre holds 1000 litres of water, what is the capacity of the trough in litres?  (1 mark)

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a.    \(3\ \text{m}^3\)

b.    \(\text{3000 litres}\)

Show Worked Solution
a.    \(\text{Volume}\) \(=Ah\)
    \(=(0.5\times 0.75)\times 8\)
    \(=0.375\times 8\)
    \(=3\ \text{m}^3\)

 

b.    \(\text{Capacity}\) \(=1000\times 3\)
    \(=3000\ \text{litres}\)

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 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 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)

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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 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

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

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

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

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

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

\(\Rightarrow A\)