Question

a cylinder has a height that is twice the length of the diameter. the diameter of the cylinder is 10 centimeters. what is the surface area of the cylinder? type the correct answer in the box. use numerals instead of words. the surface area is square centimeters.

Explanation:

Step1: Find the radius and height

Given diameter $d = 10$ cm, so radius $r=\frac{d}{2}=\frac{10}{2}=5$ cm. Height $h = 2d=2\times10 = 20$ cm.

Step2: Recall the surface - area formula

The surface - area formula of a cylinder is $S = 2\pi r^{2}+2\pi rh$.

Step3: Calculate the two parts of the surface - area

The area of the two bases is $2\pi r^{2}=2\pi\times5^{2}=2\pi\times25 = 50\pi$ square cm.
The lateral surface - area is $2\pi rh=2\pi\times5\times20 = 200\pi$ square cm.

Step4: Calculate the total surface - area

$S=2\pi r^{2}+2\pi rh=50\pi + 200\pi=250\pi$ square cm.

Answer:

$250$