Let

r1 = 2 cm the radius of the sphere (ball)

V1 = the volume of the sphere

V1 = (4/3) * r1^3 * pi

V1 = (4/3) * 2^3 * pi

r2 = 5 cm the radius of the cone

H = the height of the cone

V2 = the volume of the cone

V2 = (1/3) * r2^2 * H * pi

V2 = (1/3) * 5^2 * H * pi

Since the same volume of material is used for the cone as for the ball we can write:

V1 = V2

Plug the values into above equation:

 (4/3) * 2^3 * pi = (1/3) * 5^2 * H * pi divide both side by pi

(4/3) * 2^3 = (1/3) * 5^2 * H

(1/3) * 5^2 * H = (4/3) * 2^3

........

click here to see the step by step solving for H

........

H = 1.28 cm

The height of the cone is 1.28 cm.