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  for the volumes of a sphere and cone respectively. A. B. C. D.

Answer 1

Volume of the sphere = (4/3) pi (5a)^3
Volume cone = (1/3) pi (3a)^2 * h (h = height).

(4/3) pi 125a^3 = (1/3) pi 9a^2 h

(4/3) * 125a^3 = (1/3) 9a^2 h

h = (4/3) * 125 a^3
-------------------- = 4 * 13.889 a
(1/3) 9 a^2

h = 55.56 cu units to nearest 1/100