Question

The cylinder shown has a volume of 150 cubic inches and its height is equal to its radius. The cylinder and the sphere shown have the same radius. What is the volume of the sphere?

Answer 1

V = 200

Explanation:

Cylinder

V = pi r^2 h

150 = pi r^2 h

We know that h = r

150 = pi r^2 r

150 = pi r^3

Divide each side by pi

150 /pi = r^3

Take the cube root of each side

( 150 / pi ) ^ 1/3 = r

3.627831679 = r

Rounding to 3.63

Now find the volume of the sphere

V = 4/3 pi r^3

Replacing r^3 with 150 /pi

V = 4/3 * pi ( 150/pi)

V = 4*150 /3

V = 200