Question

if radius of a cylinder and a cone are equal and height of a cone is half that of a cylinder.

Then find the relation between their volumes in the form of ratio.​

Answer 1

radius of cone = radius of cylinder = r

height of cone = $\frac{1}{2}$ height of cylinder  ⇒$h_{1}$ = $\frac{1}{2}$ $h_{2}$ . . . . . (1)

Volume of cone = $\frac{1}{3}$πr²h = $\frac{1}{3}$ * π * r² * $h_{1}$ . . . [from (1)]

Volume of cylinder = πr²h = π * r² * 2$h_{1}$

⇒ $\frac{1}{3}$ * π * r² * $h_{1}$ : π * r² * 2$h_{1}$

⇒ $\frac{1}{3}$ : 2 {cancelled pi, r^2 and h_1} ⇒ 1 : 6

∴ The ratio between the volumes of cone and cylinder respectively = 1 : 6

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