Simmy has a sphere whose diameter is 70 cm. She wants to reduce its capacity by eight times. What should be its radius so that its capacity is reduced by eight times?

The capacity of a sphere depends on its volume, so reducing the capacity by eight times means the new volume must be one-eighth of the original volume. Since the volume of a sphere is proportional to the cube of its radius, the new radius must be the cube root of one-eighth, or one-half, of the original radius. The original diameter is 70 cm, making the original radius 35 cm, and half of this radius is 17.5 cm. The result is 17.5 cm.

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