The volume of a solid cone is exactly equal to the total volume of three smaller cones, each with radius 4 cm and height 7 cm. What is the height of the larger cone if its radius is same as that of a smaller cone?

Using the cone volume formula, the larger cone volume is one third times pi times 4 squared times height, which equals three times the volume of one smaller cone. The volume of a smaller cone is one third times pi times 16 times 7, so the large cone must equal three times this amount. Canceling the common terms of one third, pi, and 16 from both sides leaves height equal to 3 times 7, giving a height of 21 cm.

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