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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
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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.
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