Question

The surface area of a cylinder with height 2 in. is given by the function f(x) = 2πx2 + 4πx, where x is the radius. If g(x) = 4πx gives the surface area of the side of the cylinder, which combined function gives the total surface area of the two circular bases?

A. f + g
B. g − f
C. f − g
D. f · g

Answer 1

C f - g

Explanation:

the surface area of a cylinder consists of the two circles (1 at the top, 1 at the bottom) and the surrounding "mantle", the side of the cylinder, that connects the two circles.

there are no other parts.

so, when the function for the whole surface area is

SA(x) = f(x) = 2×pi×x² + 4×pi×x

and the side/ mantle area by itself is

g(x) = 4×pi×x

then when ignoring the side/mantle area part in f(x) the only thing left of the main function f(x) is the surface area of the two circular bases.

therefore, the solution for the function of the surface area of only the two circular bases must be the main function minus the function for the side/mantle area.

=> f - g