Question

part 2 of 3
the surface of a cylindrical tank is being painted. the total surface area of a cylindrical tank is the sum of two area functions. complete parts a through c below
a. write a function that gives the total area of the two circular ends as a function of radius.
f(r) = $2\pi r^2$
(type an exact answer, using $\pi$ as needed.)
b. write a function that gives the lateral surface area of the cylinder as a function of radius.
g(r) =
(type an exact answer, using $\pi$ as needed.)

Explanation:

Step1: Recall lateral surface area formula

The lateral (curved) surface area of a cylinder is given by $2\pi r h$, where $r$ is the radius and $h$ is the height/length of the cylinder.

Step2: Substitute given length

From the image, the length of the cylinder $h = 20$ ft. Substitute this into the formula:
$g(r) = 2\pi r \times 20 = 40\pi r$

Answer:

$g(r)=40\pi r$