SAT Area and volume Practice Question 2 (Hard)

Math · Geometry and TrigonometryHard

A right circular cylinder has a volume of $128\pi$ cubic centimeters, and its height is twice its radius. The total surface area of the cylinder, including both bases, is $k\pi$ square centimeters. What is the value of $k$ ?

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Answer: 96

With $h = 2r$ , the volume is $\pi r^2 (2r) = 2\pi r^3 = 128\pi$ , so $r^3 = 64$ and $r = 4$ . Then $h = 8$ . The total surface area is $2\pi r^2 + 2\pi r h = 2\pi(16) + 2\pi(4)(8) = 32\pi + 64\pi = 96\pi$ , so $k = 96$ .

Answering $64$ counts only the lateral area and forgets the two circular bases.

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