Question

A cylinder whose height is two thirds of its diameter, has the same volume as a sphere of radius 4 cm. Calculate the radius of the base of the cylinder.

Answer 1

Given that,
Height of cylinder=`2/3`(diameter)

We know that,
Diameter= 2(radius)

`h= 2/3×2r=4/3r`

Volume of the cylinder = volume of the sphere

⇒`cancel(h)r^2×cancel(4)/cancel(3)r=cancel(4)/cancel(3)cancel(h)(4)^3`

⇒`r^3=4^3`

⇒ r=4cm