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.

 

Options

• 15 cm

• 10 cm

• 18 cm  

•  5 cm 

Answer 1

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.