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.
Given-Radius of a sphere (r)=4cm
Also , cylinder whose height is two thirds of its diameter has the same volume as the sphere.
∴ Volume of the sphere
=43πr3=43π×4×4×4cm3
=256π3cm3
Now volume of cylinder =256π3cm3
According to the question
Let height of the cylinder(h) =23(2R)=43R
∴ Volume =πR2H
=πR2×43R
=43πR3∴43πR3=256π3
⇒R3=256π3×34π=64=(4)3
∴R=4 cm
Hence radius of the cylinder=4cm