Question

A cone and a cylinder have congruent height and bases. The volume of the cone is 18. What is the volume of the cylinder? Explain please and thank you!

Answer 1

Correct Answer:

The cones are not congruent because one cone is oblique, which makes the length of the slant heights different. Having the same radius, height, and volume does not make the cones congruent when the corresponding slant heights are not equal. Congruent cones must have congruent corresponding slant heights, with all other corresponding parts being congruent.

Answer 2

The volume of a cone is given by the formula: V = 1/3 * B * h where B is the area of the base and h is the height of the cone.

The volume of a cylinder is given by the formula V = B*h where B is the area of the base and h is the height of the cylinder.

1/3 Bh = Bh because the bases and heights of the two solids are the same.

The volume of the cylinder is 3 times the volume of the cone.
3 * 18 = 54 which is the volume of the cylinder.