Danica S. answered • 06/11/19

Compassionate Tutor Specializing in Music, Writing, English, and Math

Hi Aaron! Thanks for your question!

The surface area of a cylinder is the sum of the area of both the top and bottom and the sides.

The area of the top is pi*radius^2, or pi (3x+4)^2

Simplifying, we get:

- Foil 3x+4

pi(3x+4)^2 = pi(9x^2+12x+12x+16)=pi(9x^2+24x+16)

The area of the sides = circumference *height. Imaging taking the tops off the cylinder and unrolling the middle. You get a quadrilateral made by the height and the circumference of the top.

circumference=pi(diameter)

diameter = 2(radius)=2(3x+4). Distributing, we get 6x+8=d

height =3*radius. Distributing, we get

3(3x+4)=9x+4

So area of sides= (6x+8)(9x+4)

Foiling, we get 54x^2+72x+24x+32

=54x^2+96x+32

Since surface are = 2*area of top + area of side, it would be:

2(pi(9x^2+24x+16)+54x^2+96x+3

Distributing, we get:

18pix^2+48pix+16pi+54x^2+96x+3

If you enter the pi quantities into a calculator to simplify and combine like terms, you get

56.55x^2+150.8x+50.27+54x^2+96x+3

=110.55x^2+246.8x+53.27

Please feel free to reach out with additional questions or to schedule a lesson, as I’d be happy to further explain this or any other math-related question.