### Home > INT2 > Chapter 12 > Lesson 12.2.4 > Problem12-142

12-142.

Martha is playing with a hollow plastic cone that has a diameter of $12$ inches and a height of $5$ inches. Her brother Matt snatches the cone, cuts two inches off the top, and places the cut piece upside down in the lower portion of the cone, then turns the whole thing over, as shown at right. How many cubic inches of water will fit inside the space of Martha’s upside-down redesigned solid?

Volume of the original cone
− Volume of smaller cone
-------------------------
= Volume of new cone

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

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

$≈ 164.37$ in$^3$