Question

let r be the triangular region in the first quadrant with vertices at points (0,0) , (h,0) , and (h,r) , where r and h are positive constants. which of the following gives the volume of the solid generated when region r is revolved about the x -axis?

Answer 1

options not given

Let r = height

A = h/2 * r = r h / 2 area of triangle

Centroid = r / 3 from calculus

2 π * r / 3 = 2 π r / 3 distance traveled by centroid in one revolution

r h / 2 * 2 π r / 3 = when revolving about x-axis

V = π r^2 h / 3