Question

Suppose that a sphere with radius 5a has the same volume as a cone of radius 3a. What is the height of the cone? Give your answer in terms of a. Use the formulas and for the volumes of a sphere and cone respectively.

Answer 1

Volume of the sphere: [4/3]π (r^3) = [4/3]π(5a)^3 = [4/3]π*125a^3 =

Volume of the cone: [1/3]π(r^2)H = [1/3]π(3a)^2 * H = 3πa^2 * H

Volumen of the sphere = Volumen of the cone =>

[4/3]π*125a^3 = 3πa^2 * H => H = [500/9]a = 55.55 a

 

Answer 2

Answer: its 500/9a : took the test got it right! hope this helps(:

Step-by-step explanation: