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Volume, SM-Bank 089

A large sculpture is made in the shape of a cube.

The total length of all of its edges is 60 metres.

What is the volume of the cube in cubic metres?  (2 marks)

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\(125\ \text{m}^3\)

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\(\text{A cube has 12 edges.}\)

\(\text{Length of 1 edge} =\dfrac{60}{12} = 5\ \text{m}\)
 

\(\therefore\ \text{Volume of cube}\) \(=5\times 5\times 5\)
  \(=125\ \text{m}^3\)

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 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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\(1.1\ \text{m}\)

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

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

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

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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\(0.7\ \text{m}\)

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

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

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

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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\(49\ \text{cm}\)

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

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

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

Volume SM-Bank 040

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

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\(3\ \text{mm}\)

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

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

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

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

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

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

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

Volume, SM-Bank 032

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

  

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

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

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