Volume, SM-Bank 147

A concrete half-pipe was constructed in a park. The pipe has a constant thickness 0.5 metres.

Calculate the volume of the concrete used to create the half-pipe, giving your answer to the nearest cubic metre. (2 marks)
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Calculate the capacity of the concrete used in kilolitres. (1 mark)
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a. \(19\ \text{m}^3\)

b. \(9\ \text{kL}\)

Show Worked Solution

a. \(\text{diameter large semi-circle = 4 m }\rightarrow\ \text{R = 2 m}\)

\(\text{diameter small semi-circle = 3 m }\rightarrow\ \text{r = 1.5 m}\)

\(\therefore\ V\)	\(=\dfrac{1}{2}\times\pi R^2h-\dfrac{1}{2}\times\pi r^2h\)
	\(=\dfrac{1}{2}\times\pi\times 2^2\times 7-\dfrac{1}{2}\times\pi\times 1.5^2\times 7\)
	\(=19.242\dots\)
	\(\approx 19\ \text{m}^3\ (\text{nearest m}^3)\)

b. \(\text{1 kL = 1 m}^3\)

\(\therefore\ 19\ \text{m}^3\)

\(=19\ \text{kL}\)