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?

Answer 1

The formula for surface area of a cylinder is:2
`A=2\pi rh + 2\pi r^(2)`
So, to solve this, we plug in what we know and solve

`A=2\pi (2x + 3)(3(2x + 3)) + 2\pi (2x + 3)^(2)`

`A=6\pi (4x^(2)+12x+9) + 2\pi (4x^(2)+12x+9)`

`A=24x^(2)\pi+72x\pi+54\pi + 8x^(2)\pi+24x\pi+18\pi`

`A=32x^(2)\pi+96x\pi+70\pi`
This is as far as we can go, because we do not know the value of x. If we did, we could solve for the surface area