Transcript The right circular cone above is sliced horizontally forming two pieces, each of which has the same height.

The right circular cone above is sliced horizontally forming two pieces, each of
which has the same height. What is the ratio of the volume of the smaller piece to
the volume of the larger piece?
(a)
(b)
(c)
(d)
(e)
Correct Answer: D
Explanation:
It is helpful to label the figure.
The top piece is a cone whose height h is one-half the height of the original cone 2h.
Using the properties of similar right triangles, you should realize the radii of these two
cones must be in the same ratio. So if the top cone has radius r, the original cone has
radius 2r.
The volume of the top piece is equal to
The volume of the bottom piece is equal to
the volume of the original cone minus the volume of the top piece.
The ratio of the volume of the smaller piece to the volume of the larger piece is