{"@context":"https://schema.org/","@type":"Quiz","name":"

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

","comment":{"@type":"Comment","text":"

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 $V=Ah$. The area of a circle can be found using the formula $A=\\pi r^{2}$, 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 $A=\\pi(4)^{2}$, 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 $V=Ah$ gives $V=16\\pi(12)$, 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.

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

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$16\\pi$

"},{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$96\\pi$

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$768\\pi$

"}],"acceptedAnswer":{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$192\\pi$

","comment":{"@type":"Comment","text":"

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