Discussion
The diameter of the base and the slant height of a right circular cone are 15 cm and 12.5 cm, respectively. Find the volume (in cm3) of the given cone.
Answer: A
The base diameter is 15 cm, so the radius is 7.5 cm and the slant height is 12.5 cm. The height follows from the right triangle.
\[ h = \sqrt{12.5^2 - 7.5^2} = \sqrt{100} = 10 \]
\[ V = \tfrac{1}{3}\pi (7.5)^2 (10) = 187.5\pi \]
The volume is 187.5 pi cubic centimetres. The option 562.5 pi is three times as much and comes from leaving out the factor one third.
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