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.

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.