Volume, SM-Bank 152

The 3D shape below is a composite prism consisting of a half-cylinder and a rectangular prism.

Calculate the volume of the of the prism in cubic centimetres, giving your answer correct to one decimal place. (2 marks)

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\( 4881.7\ \text{cm}^3\ (\text{1 d.p.})\)

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\(\text{Diameter of cylinders = 10 cm }\longrightarrow\ r=5\ \text{cm}\)

\(\text{Volume = rectangular prism + ½ cylinder}\)

\(\therefore\ V\)	\(=l\times b\times h+\dfrac{1}{2}\times\pi r^2h\)
	\(=24\times 6.5\times 25+\dfrac{1}{2}\times\pi\times 5^2\times 25\)
	\(=3900+981.747\dots\)
	\(=4881.747\dots\)
	\(\approx 4881.7\ \text{cm}^3\ (\text{1 d.p.})\)