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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)
Show Answers Only

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 094

Two identical solid cubes are placed at the bottom of a fish tank.
 

 

The fish tank is then completely filled, as shown below.

What is the volume of the water that surrounds the cubes?

Give your answer in cubic centimetres.  (2 marks)

Show Answers Only

\(185\ 250\ \text{cm}^3\)

Show Worked Solution
\(\text{Volume of tank}\) \(=l\times b\times h\)
  \(=80\times 60\times 40\)
  \(=192\ 000\ \text{cm}^3\)

 

\(\text{Volume of cubes}\) \(=2\times s^3\)
  \(=2\times 15^3\)
  \(=6750\ \text{cm}^3\)

 

\(\therefore\ \text{Volume of water}\) \(=192\ 000-6750\)
  \(=185\ 250\ \text{cm}^3\)

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)

Show Answers Only

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 088 MC

Alan is moving house and is packing his belongings in rectangular cardboard boxes.

The height of each box is 0.5 metres.

Which box has a volume of 0.12 cubic metres?
 

 

Show Answers Only

\(D\)

Show Worked Solution

\(\text{Volume}\)

\(=0.4\times 0.6\times 0.5\)

\(= 0.12\ \text{m}^3\)

\(\Rightarrow D\)

Volume, SM-Bank 087 MC

Two bricks can be joined to make three different rectangular prisms. Two of them are shown here.
 

 
What would be the measurements of the third prism?

  1. 18 cm by 16 cm by 7 cm
  2. 36 cm by 8 cm by 7 cm
  3. 32 cm by 18 cm by 7 cm
  4. 36 cm by 14 cm by 8 cm
Show Answers Only

\(B\)

Show Worked Solution

\(\text{36 cm by 8 cm by 7 cm}\)
 

\(\Rightarrow B\)

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 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 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

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

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

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

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

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

\(\Rightarrow A\)

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)

Show Answers Only

\(24320\ \text{cm}^3\)

Show Worked Solution
\(V\) \(=Ah\)
  \(=32\times 40\times 19\)
  \(=24320\ \text{cm}^3\)

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)

Show Answers Only

\(37.44\ \text{m}^3\)

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

Volume, SM-Bank 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)

Show Answers Only

\(144\ \text{cm}^3\)

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