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Volume, SM-Bank 165

The cylinder and rectangular prism below both have the same volume.
 

  1. Calculate the volume of the cylinder in cubic centimetres, correct to 2 decimal places.  (2 marks)

  2. Calculate the length of the side labelled \(\large x\), in the rectangular prism. Give your answer correct to 1 decimal place.  (2 marks)
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a.    \(314.16\ \text{cm}^3\ \text{(2 d.p.)}\)

b.    \(9.8\ \text{cm (1 d.p.)}\)

Show Worked Solution
 

a.    \(\text{Diameter = 10 cm }\longrightarrow\ \text{Radius = 5 cm}\)

\(V\) \(=\pi r^2h\)
  \(=\pi\times 5^2\times 4\)
  \(=314.159\dots\)
  \(\approx 314.16\ \text{(2 d.p.)}\)

 
\(\therefore\ \text{The volume of the cylinder is approximately 314.16 cm}^3\)
 

b.    \(V\) \(=l\times b\times h\)
  \(314.16\) \(=8\times x\times 4\)
  \(314.16\) \(=32x\)
  \(\therefore\ x\) \(=\dfrac{314.16}{32}\)
    \(=9.8175\)
    \(\approx 9.8\ \text{(1 d.p.)}\)

 
\(\therefore\ \text{The side labelled }x\ \text{is approximately 9.8 cm in length}\)