Q. 14.1( 9 Votes )
Write whether True or False and justify your answer
The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.
Answer :
Let’s check:
We have a sphere and a cylinder.
Let height of the cylinder = diameter of the cylinder = x …(i)
Then according to the question, diameter of the sphere = x
This means, radius of the sphere = x/2 …(ii)
Also, radius of the cylinder = x/2 …(iii)
We know, volume of sphere is given by
Volume1 (say) = 4/3 πr3
where r = radius of the sphere
⇒ Volume1 = 
[from (ii)] …(iv)
And Volume of cylinder is given by
Volume2 (say) = πR2h
where R = radius of cylinder
⇒ Volume2 = 
[from (i) & (iii)] …(v)
From equations (iv) & (v), we get
⇒ Volume of sphere = 2/3 (Volume of cylinder)
Thus, justified.
Hence, it is true.
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