Volume, SM-Bank 148

A large machinery storage shed has been constructed on a property. The shed is made up of a rectangular prism and a half cylinder.

Calculate the volume of the machinery shed, giving your answer to the nearest cubic metre. (2 marks)

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\(3126\ \text{m}^3\)

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\(\text{Diameter semi-circle = 12 m }\rightarrow\ \text{r = 6 m}\)

\(\therefore\ V\)	\(=\dfrac{1}{2}\times\pi r^2h+l\times b\times h\)
	\(=\dfrac{1}{2}\times\pi\times 6^2\times 19+12\times 9\times 19\)
	\(=1074.424\dots+2052\)
	\(=3126.424\dots\)
	\(\approx 3126\ \text{m}^3\ (\text{nearest m}^3)\)