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in Surface Areas And Volumes by (26.9k points)
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If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is : 

A. 2r 

B. 3r 

C. r 

D. 4r

1 Answer

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Best answer

Option : (A) 

Volume of a sphere = \(\frac{4}{3}\)πr3 

Volume of a solid cone = \(\frac{1}{3}\)πr2

Given, 

solid sphere of radius r is melted and cast into the shape of a solid cone of height r 

Let the base radius be A. 

\(\frac{4}{3}\)πr3 = \(\frac{1}{3}\)π × A2 × r 

⇒ A = 2r

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