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Volume, SM-Bank 006

A tent with semicircular ends is in the shape of a prism. The diameter of the ends is 1.5 m. The tent is 2.5 m long.
 

GEOMETRY, FUR1 2008 VCAA 6 MC

Calculate the total volume of the tent in cubic metres, correct to one decimal place.  (2 marks)

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\(2.2\ \text{m}^3\ \text{(1 d.p.)}\)

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\(\text{Diameter}=1.5\ \text{metres}\ \ \Rightarrow\ \ \ \text{Radius}= \dfrac{1.5}{2} = 0.75\ \text{metres}\)

\(V\) \(=\dfrac{1}{2}\times \pi r^2h\)
  \(=\dfrac{1}{2}\times \pi\times 0.75^2\times 2.5\)
  \(=2.2089\dots\)
  \(\approx 2.2\ \text{m}^3\ \text{(1 d.p.)}\)