A cone and a sphere have equal volumes. If the cone's height is twice its radius, what is the ratio of the cone's radius to the sphere's radius?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. ∛2 : 1.
Radius of cone = r and Height of cone (h) = 2r
Radius of sphere = R
Volume of cone = (1/3)πr2h
Volume of sphere = (4/3)πR3
(1/3)πr2h = (4/3)πR3
⇒ (1/3)πr2(2r) = (4/3)πR3
⇒ 2πr3 = 4πR3
⇒ r3 = 2R3
⇒ r3/R3 = 2/1
⇒ r : R = ∛2 : 1