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.
diameter = 2(radius)=2(3x+4). Distributing, we get 6x+8=d
height =3*radius. Distributing, we get
So area of sides= (6x+8)(9x+4)
Foiling, we get 54x^2+72x+24x+32
Since surface are = 2*area of top + area of side, it would be:
Distributing, we get:
If you enter the pi quantities into a calculator to simplify and combine like terms, you get
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.