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?
The surface area of a cone is [tex]A= \pi r^{2}+ \pi r \sqrt{ h^{2} + r^{2} } [/tex]. Lateral area is [tex]A= \pi r \sqrt{ r^{2} + h^{2} } [/tex]. Here [tex] \sqrt{ h^{2} + r^{2} } [/tex] is a slant height.
Using this information we can write that [tex]60 \pi =10 \pi r[/tex] and r=6 cm
The volume of the sphere is given by [tex]V= \frac{4}{3} \pi r^{3} [/tex]. If we calculate it, we'll obtain [tex]V=288 \pi [/tex]
