Question

Find the surface area of a cylinder with a base diameter of 10 yd and a height of 6 yd.Write your answer in terms of π, and be sure to include the correct unit.

Answer 1

The radius of the cylinder is,

$r=\frac{d}{2}$

where d is the base diameter.

Substituting the known values,

$\begin{gathered} r=\frac{10}{2} \\ r=5\text{ yd} \end{gathered}$

The height of the cylinder is,

$h=6\text{ yd}$

Thus, the surface area of the cylinder is,

$S=2\pi rh+2\pi r^2$

Substituting the known values,

$\begin{gathered} S=2\pi\times5\times6+2\pi\times5^2 \\ S=60\pi+50\pi \\ S=110\pi yd^2 \end{gathered}$

Thus, the surface area of the cylinder is,

$110\pi yd^2$