Question

The volume of a cone varies jointly as the square of its radius and its height. If the volume of a cone is 2 pi cubic inches when the radius is 1 inch and the height is 6 inches, find the volume of a cone when the radius is 5 inches and the height is 3 inches. Please help!!!!!!! :(

Answer 1

The variation statement tells you that when the radius is multiplied by 5, the volume is multiplied by 5² = 25. When the height is multiplied by 1/2, the volume is multiplied by 1/2.

Both of these variations together will multiply the volume by 25·(1/2) = 25/2.

So, the revised volume is (2π in³)·25/2 = 25π in³.