The radius of a cylindrical gift box is (3x+2) 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.

Answer 1

The surface area of a cylinder is given by the formula:

SA = 2πr^2 + 2πrh

where r is the radius and h is the height.

In this case, the radius is (3x+2) inches and the height is 3 times the radius, or 3(3x+2) = 9x+6 inches.

Substituting these values into the formula, we get:

SA = 2π(3x+2)^2 + 2π(3x+2)(9x+6)

Simplifying this expression, we get:

SA = 18πx^2 + 60πx + 24π

Therefore, the surface area of the cylinder is 18πx^2 + 60πx + 24π square inches.