Volume, SM-Bank 157

A right cylinder has a volume of 8482.3 cubic millimetres. Calculate the diameter of the cylinder if the height is 12 millimetres.

Give your answer to the nearest whole millimetre. (3 marks)

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\(30\ \text{mm}\)

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\(V\)	\(=\pi r^2h\)
\(8482.3\)	\(=\pi\times r^2\times 12\)
\(8482.3\)	\(=12\pi\times r^2\)
\(r^2\)	\(=\dfrac{8482.3}{12\pi}\)
\(r^2\)	\(=224.999\dots\)
\(r\)	\(=\sqrt{224.999}=14.999\dots\)
\(r\)	\(\approx 15\ \text{mm (nearest whole mm)}\)

\(\therefore\ \text{The diameter of the cylinder is approximately 30 mm}\)