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

Let radius of cylinder = r. Diameter of cylinder = 2r

Height of cylinder =
`(2)/(3) (2r)= (4r)/(3)` .....[Given]
Volume of cylinder =
`\pi x^(2) h= \pi x^(2) ( (4r)/(3) )= (4 x^(3) )/(3)`
Volume of sphere with radius 4 cm =
`(4)/(3) \pi (4) ^(3) = (4)/(3) \pi (64)`

According to the question,
Volume of cylinder = Volume of sphere
=>
`(4)/(3) \pi x^(3) = (4)/(3) \pi (4) ^(3) =\ \textgreater \ r^(3) =(4)^(3) =\ \textgreater \ r = 4cm`

Hence, radius of base of cylinder = 4cm