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# 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. - Geometry

#### 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?