Question

A cylinder has a radius of 2x + 3 and a height of 6x + 1. Which polynomial in standard form best describes the total volume of the cylinder? use the formula v=pir^2h for the volume of a cylinder

Answer 1

24pi x^3 +76pi x^2 +66pi x +9pi

Answer 2

The volume of a cylinder is expressed as V = πr^2h where r is the radius and is half the diameter and h is the height of the cylinder. We are given expression for each dimension of the shape. Substituting,

V = πr^2h
V = π(2x+3)^2 (6x + 1)
V = π (4x^2 + 12x + 9) (6x + 1 )
V = π (24x^3 + 4x^2 + 72x^2 + 12x + 54x + 9 )
V = π (24x^3 + 76x^2 + 66x + 9 )