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Geometry and Trigonometry / Area and volume Difficulty: Hard

The circumference of the base of a right circular cylinder is $20 pi$ meters, and the height of the cylinder is $6$ meters. What is the volume, in cubic meters, of the cylinder?

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Explanation

Choice C is correct. The volume, $V$ , of a right circular cylinder is given by the formula $V = π r^{2} h$ , where $r$ is the radius of the base of the cylinder and $h$ is the height of the cylinder. It’s given that a right circular cylinder has a height of $6$ meters. Therefore, $h equals 6$ . It's also given that the right circular cylinder has a base with a circumference of $20 pi$ meters. The circumference, $C$ , of a circle is given by $upper C equals 2 pi r$ , where $r$ is the radius of the circle. Substituting $20 pi$ for $C$ in the formula $upper C equals 2 pi r$ yields $20 pi equals 2 pi r$ . Dividing each side of this equation by $2 pi$ yields $10 equals r$ . Substituting $10$ for $r$ and $6$ for $h$ in the formula $V = π r^{2} h$ yields $upper V equals pi left parenthesis 10 right parenthesis squared left parenthesis 6 right parenthesis$ , or $upper V equals 600 pi$ . Therefore, the volume, in cubic meters, of the cylinder is $600 pi$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect. This is the lateral surface area, not the volume, of the cylinder.

Choice D is incorrect. This is the result of using the diameter, not the radius, for the value of $r$ in the formula $V = π r^{2} h$ .