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Geometry and Trigonometry Difficulty: Medium

A right circular cylinder has a volume of $432$ cubic centimeters. The area of the base of the cylinder is $24$ square centimeters. What is the height, in centimeters, of the cylinder?

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Explanation

Choice A is correct. The volume, $V$ , of a right circular cylinder is given by the formula $V = π r^{2} h$ , where $π r^{2}$ is the area of the base of the cylinder and $h$ is the height. It’s given that a right circular cylinder has a volume of $432$ cubic centimeters and the area of the base is $24$ square centimeters. Substituting $432$ for $V$ and $24$ for $π r^{2}$ in the formula $V = π r^{2} h$ yields $432 equals 24 h$ . Dividing both sides of this equation by $24$ yields $18 equals h$ . Therefore, the height of the cylinder, in centimeters, is $18$ .

Choice B is incorrect. This is the area of the base, in square centimeters, not the height, in centimeters, of the cylinder.

Choice C is incorrect. This is the height, in centimeters, of a cylinder if its volume is $432$ cubic centimeters and the area of its base is $2$ , not $24$ , cubic centimeters.

Choice D is incorrect. This is the height, in centimeters, of a cylinder if its volume is $432$ cubic centimeters and the area of its base is $\frac{1}{24}$ , not $24$ , cubic centimeters.