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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 Answer

  1. Given,

    Radius of the copper sphere = 3 cm

    We know that,

    Volume of the sphere = 4/3 π r3

    = 4/3 π × 33 ….. (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 π r2h

    = 1/3 π × r2 × 3 ….. (ii)

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

    4/3 π × 33 = 1/3 π × r2 × 3

    r2 = 36

    r = 6 cm

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

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