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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