Question

the radii of two cylinders are in the ratio of 1:$\sqrt{3}$ . if the volume of the two cylinders are the same, then what are the ratio of their heights?

Answer 1

let radius 1 be r and 2 be R

Hence, r:R::1:√3

let height of cylinder 1 be h amd 2 be H

let volume of cylinder 1 be v

v= πr^2h

v= volume of cylinder 2(given)

πr^2h=πR^2H

πr^2h/πR^2=H

(1/√3)^2= H

1/3=H