Question

the surface of a cylindrical tank is being painted. the total surface area of a cylindrical tank is the sum of two area functions 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.
$g(r) = 40\pi r$
(type an exact answer, using $\pi$ as needed.)

c. combine the functions from parts a and b to get the total surface area of the cylinder as a function of radius.
$(f + g)(x) = $
(type an exact answer, using $\pi$ as needed. do not factor)

Explanation:

Step1: Define sum of functions

$(f+g)(r) = f(r) + g(r)$

Step2: Substitute given functions

$(f+g)(r) = 2\pi r^2 + 40\pi r$

Answer:

$2\pi r^2 + 40\pi r$