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Home > INT2 > Chapter 12 > Lesson 12.2.4 > Problem 12-142


Martha is playing with a hollow plastic cone that has a diameter of inches and a height of 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

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


Upward cone, with top part of the cone removed,  labeled, original view. The top shows a solid circle, with the top part of the cone, outlined downward, from the top circle. The same drawing, but as a downward cone, is labeled, original view upside-down.