Volume; disk method

Question

Suppose you are given a solid whose base is the circle x^2+y^2=64 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal.

Find the area of the vertical cross section A at the level x=3.

A=

Find the volume V of the solid.

V=

Thank you in advance!

Answer 1

a) The cross sections are perpendicular to x and have a base of 2y and a height of 2y. Their area will be 1/2(2y)² = 2y²

at x = 3 y² = 64 - 3² and A = 2y²

b) The volume of the solid is just Integral from -8 to 8 of A(x)dx

By substitution of A(x) = 2y² = 2(64-x²) , you can solve the reasonable integral after multiplying out.

Please consider a tutor.