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A cone has a slant height of 10 centimeters and a lateral area of 60π square centimeters. what is the volume of a sphere with a radius equal to that of the cone?

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The surface area of a cone is
A= \pi r^(2)+ \pi r \sqrt{ h^(2) + r^(2) }. Lateral area is
A= \pi r \sqrt{ r^(2) + h^(2) }. Here
\sqrt{ h^(2) + r^(2) } is a slant height.

Using this information we can write that
60 \pi =10 \pi r and r=6 cm

The volume of the sphere is given by
V= (4)/(3) \pi r^(3). If we calculate it, we'll obtain
V=288 \pi
User Elia Weiss
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