#### Question

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.

15 cm

10 cm

18 cm

5 cm

#### Solution

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.

∴ 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.

Is there an error in this question or solution?

Solution 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. Concept: Problems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle.