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Geometry and Trigonometry / Area and volume Difficulty: Medium

A cylinder has a diameter of $8$ inches and a height of $12$ inches. What is the volume, in cubic inches, of the cylinder?

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Explanation

Choice C is correct. The base of a cylinder is a circle with a diameter equal to the diameter of the cylinder. The volume, $V$ , of a cylinder can be found by multiplying the area of the circular base, $A$ , by the height of the cylinder, $h$ , or $V = A h$ . The area of a circle can be found using the formula $A = π r^{2}$ , where $r$ is the radius of the circle. It’s given that the diameter of the cylinder is $8$ inches. Thus, the radius of this circle is $4$ inches. Therefore, the area of the circular base of the cylinder is $upper A equals pi left parenthesis 4 right parenthesis squared$ , or $16 pi$ square inches. It’s given that the height $h$ of the cylinder is $12$ inches. Substituting $16 pi$ for $A$ and $12$ for $h$ in the formula $V = A h$ gives $upper V equals 16 pi left parenthesis 12 right parenthesis$ , or $192 pi$ cubic inches.

Choice A is incorrect. This is the area of the circular base of the cylinder.

Choice B is incorrect and may result from using $8$ , instead of $16$ , as the value of $r^{2}$ in the formula for the area of a circle.

Choice D is incorrect and may result from using $8$ , instead of $4$ , for the radius of the circular base.