Question

a cylinder has a diameter of 6 inches and a height of 21 inches. what is the volume, in cubic inches, of the cylinder? a 9π b 126π c 189π d 756π

Explanation:

Step1: Find the radius

The radius $r$ of a circle is half of the diameter. Given diameter $d = 6$ inches, so $r=\frac{d}{2}=\frac{6}{2}=3$ inches.

Step2: Use the volume formula for a cylinder

The volume formula of a cylinder is $V=\pi r^{2}h$. Substitute $r = 3$ inches and $h=21$ inches into the formula. We get $V=\pi\times3^{2}\times21$.

Step3: Calculate the volume

First, $3^{2}=9$. Then $V=\pi\times9\times21 = 189\pi$ cubic - inches.

Answer:

C. $189\pi$