A sphere with a radius of 6 cm has the same volume as a cone with a height of 6 cm. What is the radius of the cone?

Answer 1

Formulas needed: Volume of a Sphere V=(4/3)pi (r)^3 Volume of a cone V=(1/3) pi (r)^2 h

First calculate the volume of the cone. There's only one variable, r, which is given as 6

V=(4/3) pi (6^3)=904.78 or =288(pi)

Now sub that value in for V in the cone equation, also subbing in 6 for the h

288(pi)=(1/3) pi (r)^2 (6)

Use algebra to solve for r