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 \: r {}^(2) h = \pi \: r {}^(2) ( (4\pi)/(3) ) = \frac{4\pi \: r {}^(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 \: r {}^(3) = (4)/(3) \pi(4) {}^(3)`
=>
`r {}^(3) = (4) {}^(3)`
=> r = 4

Hence,radius of base of cylinder = 4 cm