The base of a solid is a circular disk with radius 3 . Find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypotenuse lying along the base.
A) 6
B) 7
C) 16
D) 49
E) None of these

Question

Quizplus · Accepted Answer

The volume of the solid is calculated by integrating the area of the cross-sections. The hypotenuse of each isosceles right triangle is a chord of the circle, and the side length of the triangle is the hypotenuse divided by √2. The area of each triangle is (1/2) * (side length)^2. Integrating this area over the circle's diameter gives a volume of 9π, which is not listed among the choices.

The Base of a Solid Is a Circular Disk with Radius