Question

A sphere and the right circular cylinder same radius have equal volumes by what percentage does the diameter of cylinder exceeds height.​

Answer 1

The diameter of the cylinder exeeds it's height by 33.3%

i) Let the radius of the cylinder and the sphere be r , height of the cylinder be h and diameter of the cylinder be d.

ii) According to the question:

Volume of sphere = Volume of cylinder

(4/3)πr^3 = πr^2h

iii) Solving the above equation we get;

2r = (3/2) h

d = (3/2) h

iv) percentage increase of the cylinder's diameter by it's height can be calculated

as follows:

% increase = [(d-h) /d]×100

= [(3h/2 - h) /3h/2]×100

= 33.3%