Question

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

What is the answer?

Answer 1

`S(x)=32\pi x^2+96\pi x+72\pi`

Explanation:

The surface area of a cylinder is given as
`S.A=2\pi r(r+h)`

We have that the radius of the box is
`r=2x+3` inches.

The height of the gift box is three times the radius.

`\implies h=3(2x+3)\\\implies h=6x+9`

We substitute into the formula to get:

`S.A=2\pi (2x+3)(2x+3+6x+9)`

We simplify the last parenthesis to get:

`S.A=2\pi (2x+3)(8x+12)`

We expand the last two binomial factors to get:

`S.A=2\pi(16x^2+48x+36)`

We expand further to get:

`S.A=32\pi x^2+96\pi x+72\pi`