Volume, SM-Bank 151

A piece of metal in the shape of a rectangular prism has had two cylindrical holes, each with a diameter of 8 millimetres, drilled through it.

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

--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

\( 4937.6\ \text{mm}^3\ (\text{1 d.p.})\)

Show Worked Solution

\(\text{Diameter of cylinders = 8 mm }\longrightarrow\ r=4\ \text{mm}\)

\(\text{Volume = rectangular prism – 2 × cylinders}\)

\(\therefore\ V\)	\(=l\times b\times h-2\times\pi r^2h\)
	\(=32\times 16\times 12-2\times\pi\times 4^2\times 12\)
	\(=6144-1206.371\dots\)
	\(=4937.628\dots\)
	\(\approx 4937.6\ \text{mm}^3\ (\text{1 d.p.})\)