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Question

A right cylinder is inscribed in a sphere with radius 10 if radius of circular base of cylinder is 6 what is vol of cylinder

Answer 1

Draw a radius from the center of the sphere to a point where the cylinder intersects the sphere.  This is the hypotenuse of a right triangle with horizontal leg equal to the radius of the base of the cylinder and vertical leg, v, which is half the height of the cylinder.

 

By the Pythagorean Theorem, v² + 6² = 10²

 

                                                    v² = 64

 

                                                    v = 8

 

Height of cylinder = 16

 

Volume of cylinder = π(radius of base)²(height) = π(6)²(16)

 

                                                                     = 576π