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# A copper sphere of radius 3 cm is melted and recast into a right circular cone of height 3 cm. Find the radius of the base of the cone?

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One of the important question for the board exam class 10 from mensuration chapter.
This question is from r d sharma class 10 maths.
chapter-16 question number-16 maths r d sharma,mensuration.
In this question we have to find the radius of the base of the cone having a copper sphere of radius 3 cm is melted and recast into a right circular cone of height 3 cm.

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1. Given,

Radius of the copper sphere = 3 cm

We know that,

Volume of the sphere = 4/3 Ï€ r3

= 4/3 Ï€ Ã— 33 â€¦.. (i)

Also, given that the copper sphere is melted and recasted into a right circular cone

Height of the cone = 3 cm

We know that,

Volume of the right circular cone = 1/3 Ï€ r2h

= 1/3 Ï€ Ã— r2 Ã— 3 â€¦.. (ii)

On comparing equation (i) and (ii) we have,

4/3 Ï€ Ã— 33 = 1/3 Ï€ Ã— r2 Ã— 3

r2 = 36

r = 6 cm

Therefore, the radius of the base of the cone is 6 cm.

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