MATH-182 Lecture 3: MATH 182 Lecture 3: Calculus II: Area bounded by lines cont. and Volumes of Solids

Equal Volumes

Let and be the volumes of the solids that result when the plane region bounded by  is revolved about the x-axis and the y-axis respectively. Find the value of c for which .

Find the volumes of the solids whose bases are bounded by thecircle x² + y² =9, with the indicated crosssections taken perpendicular to the x-axis.

a. Squares?

b.equilateral triangles?

c. Semicircles?

d. Isosceles right triangles?

Find the volumes of the solids obtained by rotating the region bounded by the curves and about the following lines.

1. The x-axis (b) The y-axis (c)