The radius of a cylindrical gift box is (2x+3) in. The height of the gift box is twice the radius. What is the surface area of the cylinder? Write your answer as a polynomial form.

Verified Answer :

let "r" be the radius of cylinder and "h" be the height.
Formula for surface area is:

S= 2r^2pi + 2rpih

where 2
4^2pi is surface of two bases of cylinder and 2rpih is surface of mantle.
One of the tasks conditions is that h = 2r.

S = 2
r^2pi + 2r2rpi

second and last condition is r=(2x+3). Now we express this as well.

S = 2
(2x + 3)^2 pi + 4(2x+3)^2pi=6pi(2x+3)^2

S = 6
pi(4x^2+12x + 9)
S = 24
pix^2 + 72pix + 54pi