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Question

504 cones each of diameter 3.5 and height 3cm are melted and recast into a metallic sphere find the diameter of the sphere and hence its surface area

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Solution

Answer :

Height of cone = 3 cm
And
Diameter of cone = 3.5 cm , So radius of cone = 3.52 cm
And we know Volume of cone = π r2 h3
So,
Volume of a cone = 227× 3.52×3.52×33 = 11 × 0.5 × 3.52 = 19.252 = 9.625 cm3
And
We know Volume of sphere = 4 π r33 , Here r radius of sphere
From given condition we get

Volume of metallic sphere = 504 ( Volume of a cone ) , So

4×227×r33 = 504× 9.62588×r321 =4851r321 =55.125 r3 = 1157.625 r=1157.6253 r= 10.50 cmSo, Diameter ( d ) = 2r = 2 × 10.50 = 21 cm ( Ans )
And
we know Surface area of sphere = 4 π r2
So,
Surface area of our sphere = 4 ×227×10.5×10.5 = 4 × 22 × 1.5 × 10.5 = 1386 cm2 ( Ans )

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