Expert: Steve Holleran - 11/4/2007

Question
A sphere has a radius of 6.8cm. A cone has a base radius of 9.6cm. The volume of the sphere is equal to the volume of the cone. Calculate the height of the cone, h, giving your answer correct to 3 significant figures.

Thanks in advance.

Answer
Hi Hassan,

Okay, the formulas are:

Sphere :  V = 4/3 * pi * r^3

Cone:     V = 1/3 * pi * r^2 * h

So, for the sphere we have

        V = 4/3 * pi * 6.8^3

and for the cone

        V = 1/3 * pi * 9.6^2 * h

Setting them equal, you can cancel the pi's and multiply each side by 3, getting

         4 * 6.8^3 = 9.6^2 * h

so        h = (4 * 6.8^3) / 9.6^2 = 13.6472.

Don't know much about significant figures, so you can decide how many to include.  I would just say 13.6

Steve