Find the volume of the solid whose base is the semicircle y=sqrt(16−x^2) where −4 is less then or equal to x which is less then or equal to 4, and the cross sections perpendicular to the x-axis are squares.

Question

Find the volume of the solid whose base is the semicircle y=sqrt(16−x^2)  where −4 is less then or equal to x which is less then or equal to 4, and the cross sections perpendicular to the x-axis are squares.

Mgraph · Answer

Lengths of the sides of these squares are equal to y. The volume=Int(from -4 to 4)y^2dx= 2*Int(from 0 to 4)(16-x^2)dx= 2*(16x-x^3/3)(from 0 to 4)= 2(64-64/3)