The surface area of a solid metallic sphere is 616 cm2.

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asked Mar 27 in Class X Maths by muskan15 (-3,369 points)

The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into smaller spheres of diameter 3.5 cm. How many such spheres can be obtained ?

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answered Mar 27 by navnit40 (-4,348 points)

The surface area of sphere = 4πr2

4πr2 = 616

r2 = 616 × 7/4 × 22 = 49

r = √49

r = 7 cm

Vol. of big sphere  = 4/3πr3 = 4/3 × 22/7 × (7)3

Vol. of small sphere = 4/3π(3.5/2)3

∴  No. of smaller sphere = Vol. of big sphere/Vol. of small sphere

= (4/3π(7)3)/(4/3π(3.5/2)3)

= 64

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