Question

A sphere and a right circular cone of same radius have equal volumes. By what percentage does the height of the cone exceed its diameter ?

(a) 50 % 

(b) \(66\frac13\)%

(c) 100 % 

(d) 43.75%

Answer 1

(c) 100%

Let r be the radius of the cone and sphere. 

Let h be the height of the cone. 

Then, according to the question, 

\(\frac43πr^3=\frac13πr^2h\) ⇒ h = 4r 

∴ Required % difference = \(\big(\frac{4r-2r}{2r}\times100\big)\)% = 100%.