A cylinder and a cone are shown below. Which explains whether the bases of the cylinder and the cone have the same area?

Question

A. The bases have the same area because the heights are the same.
B. The bases have the same area because the volume of the cone is mc014-2.jpg the volume of the cylinder.
C. The bases do not have the same area because the volumes are not the same.
D. The bases do not have the same area because the volume of the cylinder is not 3 times the volume of the cone, given the same heights.

Answer 1

Kaitlyn,

 

Hi!  The answer is letter 'D' because in the cone formula, the height times the base (area) is divided by three.  In the cylinder volume formula, the base (area) is multiplied by the height (no division by 3).  If you would have the same areas of bases in both the cylinder and the cone, the area of the cylinder would be three times (3768 in^3) the area of the cone and it is not!