Question

find the surface area of a cylinder with a base radius of 6 yd and a height of 9 yd. write your answer in terms of π, and be sure to include the correct unit.

Explanation:

Step1: Find area of two bases

The area of a circle is $A = \pi r^{2}$. For two bases, $A_{bases}=2\pi r^{2}$. Substituting $r = 6$ yd, we get $A_{bases}=2\pi\times6^{2}=72\pi$ square - yards.

Step2: Find lateral - surface area

The lateral - surface area of a cylinder is $A_{lateral}=2\pi r h$. Substituting $r = 6$ yd and $h = 9$ yd, we get $A_{lateral}=2\pi\times6\times9 = 108\pi$ square - yards.

Step3: Calculate total surface area

The total surface area of a cylinder $A = A_{bases}+A_{lateral}$. So $A=72\pi + 108\pi=180\pi$ square - yards.

Answer:

$180\pi$ square yards