SSC (Marathi Semi-English) 10thMaharashtra State Board
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Choose the Correct Alternative Answer for Each of the Following Questions (6) a Cone Was Melted and Cast into a Cylinder of the Same Radius as that of the Base of the Cone. - SSC (Marathi Semi-English) 10th - Geometry

ConceptProblems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle

Question

Choose the correct alternative answer for each of the following questions

(6) 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.

• (A) 15 cm

• (B) 10 cm

• (C) 18 cm

• (D) 5 cm

Solution

(6) Radius of the cone = Radius of the cylinder = 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?

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Solution Choose the Correct Alternative Answer for Each of the Following Questions (6) 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.
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