Question

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

Answer 1

We know that, Volume of a sphere = `4/3 pir^3`

Where, `pi = 22/7`

r = radius of a sphere

And Volume of cylinder = πr²h

Where r = radius

And π = 3.14

Given: Volume of sphere = Volume of right circular cylinder

Thus, ⇒ `4/3 pir^3 = pir^2h`

⇒ `4/3 r = h`

⇒ `r = (3h)/4`

Multiplying by 2 on both side

⇒ `2r = 2 xx (3h)/4`

⇒ `D = (3h)/2`  ...(Since, diameter D = 2r)

Let h be 100%

Thus, `D = (3h)/2 = (3 xx 100%)/2` = 150%

Required difference = 150% – 100% = 50%

Thus, Diameter of a cylinder exceeds its height by 50%