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Geometry and Trigonometry / Area and volume Difficulty: Medium

A right circular cylinder has a height of $8 meters left parenthesis m right parenthesis$ and a base with a radius of $12 m$ . What is the volume, $in m^{3}$ , of the cylinder?

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Explanation

Choice D is correct. The volume, $V$ , of a right circular cylinder is given by $V = π r^{2} h$ , where $r$ is the radius of the circular base and $h$ is the height of the cylinder. It’s given that the cylinder has a height of $8$ meters and a base with a radius of $12$ meters. Substituting $12$ for $r$ and $8$ for $h$ in $V = π r^{2} h$ yields $upper V equals pi left parenthesis 12 right parenthesis squared left parenthesis 8 right parenthesis$ , or $upper V equals 1,152 pi$ . Therefore, the volume, in $m Superscript 3$ , of the cylinder is $1,152 pi$ .

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

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

Choice C is incorrect. This is the volume, in $m Superscript 3$ , of a cylinder with a radius of $8$ meters and a height of $12$ meters.