A spherical metal of radius 10 cm is molten and made into 1000 smaller spheres of equal sizes. In this process the surface area of the metal is increased by:
Explanation:
Let r be the radius of the smaller sphere. Now, the volume of the big sphere and the 1000 small spheres is same. Hence, we have, Hence, r3 = 1 Hence, r = 1 Now, total surface area of big sphere = 4 × π × 102 = 400π Total surface area of 1000 new sphere = 1000 × 4π × 12 = 4000π Hence, total surface area increases by, (4000π – 400π) / 400π = 9 times. Hence, option (e).
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