The sphere's radius is one-third the radius of the hemisphere. How does the volume of this hemisphere compare with the volume of the sphere?
Accepted Solution
A:
Volume of the sphere = 3/4 pi r^3
The spheres radius is one third of the hemisphere's so radius of hemisphere = 3r Volume of the hemisphere = 1/2 * 4/3 pi (3r)^3 = 2/3 * 27 pi r^3 = 18 pi r^3 So vol hemisphere / vol sphere = 18 pi r^3 / 4/3 pi r^3 = 18 * 3/4 = 13.5
Hemisphere is 13.5 times the volume of the sphere.