Question

A cylinder has a radius of 2x + 3 and height of 3x + 2. Which polynomial in standard form best describes the total volume of the cylinder? Use the formula V= πr^2h for the volume of a cylinder.

Answer 1

`v = \pi {r}^(2) h \\ v = \pi {(2x + 3)}^(2) (3x + 2) \\ v = \pi(4 {x}^(2) + 12x + 9)(3x + 2) \\ v =( 12 {x}^(3) + 36 {x}^(2) + 27x + 8 {x}^(2) + 24x + 18)\pi \\ v =( 12 {x}^(3) + 44 {x}^(2) + 51x + 18)\pi`