CPM Homework Help : CCG Problem 11-75

Martha was playing with a hollow plastic cone that had a diameter of $12$ inches and a height of $5$ inches. Her brother Matt snatched the cone, cut two inches off the top, and placed the cut piece upside down in the lower portion of the cone as shown at right. How many cubic inches of water would fit inside the space of her redesigned cone?

Upward cone, with top part of the cone removed, labeled, original view, with the dashed outline of the top part of the cone, pointing downward, from the top cut off face. Below is a downward cone, with the point of the cone removed, labeled, original view upside-down, with the dashed outline of the cone point, pointing upward, from the bottom cut off face.

Hint:

$\array{ \qquad \qquad \quad \text{Volume of the original cone} \\ \quad \ - \quad \text{Volume of smaller cone}\\ \hline = \ \ \ \text{Volume of new cone} }$

More Help:

${\large{V}}\text{cone} = \frac{1}{3} \pi r^2h$

Hint:

Use a proportion ratio to solve for the radius of the smaller cone.

Answer:

$\approx164.37\text{ in}^3$