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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?
Solution
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%
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