Algebra and Up:
Question: Luke makes a papier mache, right-circular-cone-shaped volcano model for this science fair project. The cone is 1 foot tall before he cuts off the top, which makes the volcano 2 inches shorter. If the area of the circular base of the cone is
144π square inches, then what is the volume of the volcano model after its top has been removed?
(Hint: The volume of a cone is â…“ of the area of its base times its height.)
Answer: 573â…“π cubic inches
Solution: One way to find the difference in volume between the cut-off cone and the volume of the whole cone. The whole cone is â…“ × 144π × 12 = 576π cubic inches before the top is removed. The dimensions of the cut-off cone are 2 ÷ 12 = â…™ those of the whole. Since the base is in two dimensions, its area is â…™ × â…™ × 144π = 4π square inches. The volume of the cut-off cone is â…“ × 4π × 2 = 2â…”π cubic inches, and the difference is 573â…“π cubic inches.
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