SAT Area and volume Practice Question 6 (Medium)

Math · Geometry and TrigonometryMedium

A right circular cone has a base radius of $6$ centimeters. A sphere with a radius of $6$ centimeters has the same volume as the cone. What is the height, in centimeters, of the cone?

$8$

$18$

$24$

$32$

Show answer and explanation

Answer: C

The cone's volume is $\frac{1}{3}\pi(6)^2 h = 12\pi h$ . The sphere's volume is $\frac{4}{3}\pi(6)^3 = 288\pi$ . Setting them equal, $12\pi h = 288\pi$ , so $h = 24$ .

Choice A omits the $\frac{1}{3}$ in the cone formula, giving $36\pi h = 288\pi$ .

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