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Volume, SM-Bank 166

The cube and cylinder below both have the same volume.
  

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

  2. Calculate the height of the cylinder, \(\large h\), in centimetres. Give your answer correct to 1 decimal place.  (2 marks)
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a.    \(64\ \text{cm}^3\)

b.    \(5.1\ \text{cm (1 d.p.)}\)

Show Worked Solution
 

a.    \(V\) \(=l\times b\times h\)
    \(=4^3\)
    \(=64\)

 
\(\therefore\ \text{The volume of the cube is 64 cm}^3\)
 

b.    \(\text{Diameter = 4 cm}\ \longrightarrow\ \text{Radius = 2 cm}\)

\(V\) \(=\pi r^2h\)
\(64\) \(=\pi\times 2^2\times h\)
\(64\) \(=4\pi h\)
\(\therefore\ h\) \(=\dfrac{64}{4\pi}\)
  \(=5.092\dots\approx 5.1\ \text{(1 d.p.)}\)

 
\(\therefore\ \text{The height of the cylinder is approximately 5.1 cm}\)