Question

Sphere and right circular cylinder have same radii and equal volume. By what % does diameter of cylinder increased its height?

Answer 1

Given sphere and a right circular cyclinder of the same radius.

Volume of Sphere = (4/3)πr3

Volume of right circular cyclinder = πr2h

Given Volume of Sphere = Volume of right circular cyclinder.

(4/3)πr3 = πr2h

(4 /3) r = h.

2r = 3h / 2

d = 3h / 2

Now, let h be 100 %.

D = 3h/ 2 = (3/2)x 100% = 150%

So, required difference = 150% - 100% = 50%

Hence, diameter of the cylinder exceed its height by 50%