Choose the correct alternative answer for the following question. A cone was melted and cast into a cylinder of the same radius as that of the base of the cone. If the height of the cylinder is 5 cm, find the height of the cone.

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KollegeApply · Accepted Answer

The radius of the cone = Radius of the cylinder = r cm (Say) Height of the cylinder, h = 5 cm Let the height of the cone be H cm. It is given that the cone melted and recasted into a cylinder. $\therefore$ Volume of the cone = Volume of the cylinder \Rightarrow $\frac{1}{3}$$\pi$ r^2 H = $\pi$ r^2 h \Rightarrow H = 3h \Rightarrow H = 3 $\times$ 5 = 15 cm Thus, the height of the cone is 15 cm.

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