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

Volume_{1} (say) = 4/3 πr^{3}

where r = radius of the sphere

⇒ Volume_{1} =

[from (ii)] …(iv)

And Volume of cylinder is given by

Volume_{2} (say) = πR^{2}h

where R = radius of cylinder

⇒ Volume_{2} = [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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