Discussion
The perimeter of the base of a vessel, in the shape of a right circular cone, is \(22\pi\) cm. Its curved surface area is \(671\pi\) \(cm^{2}\). The capacity (in litres) of the vessel is
Answer: C
The capacity is 2.42 pi litres. The base perimeter is \(2\pi r = 22\pi\), so r = 11 cm. The curved surface area is \(\pi r l = 671\pi\), so \(l = 671/11 = 61\) cm. The height is \[h = \sqrt{61^2 - 11^2} = \sqrt{3600} = 60\] cm. The volume is \[\frac{1}{3}\pi r^2 h = \frac{1}{3}\pi \times 121 \times 60\] \[= 2420\pi\ \text{cm}^3\] Since 1 litre is 1000 cubic centimetres, this is 2.42 pi litres. The other options come from a wrong height or from forgetting the conversion to litres.
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