1. 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:
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By: anil on 05 May 2019 02.37 am
Radius of larger sphere = $$R = 10$$ cm Let radius of each of the smaller spheres = $$r$$ cm => $$frac{4}{3} pi R^3 = 1000 imes frac{4}{3} pi r^3$$ => $$10^3 = 1000 r^3$$ => $$r = sqrt[3]{1} = 1$$ cm Initial surface area of sphere = $$4 pi R^2 = 4 pi imes 100 = 400 pi$$ Final surface area of 1000 spheres = $$1000 imes 4 pi r^2 = 1000 imes 4 pi = 4000 pi$$ $$ herefore$$ Increase in surface area = $$4000 pi - 400 pi = 3600 pi$$ => $$frac{3600 pi}{400 pi} = 9$$ times
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