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Question 105

A solid sphere of radius 10 cm is melt and moulded into 8 solid spherical balls of equal radius. The surface area of eachball. in sq. cm. is

Solution

given,

radius of sphere=10 cm

volume of each spherical ball=$$\frac{volume of sphere}{8}$$

$$\frac{4\times \pi\times r^3}{3}$$=$$\frac{1}{8}$$ $$\frac{4\times \pi\times 10^3}{3}$$

$$r^3$$=$$\frac{1000}{8}$$

$$r^3$$=$$\frac{10^3}{2^3}$$

r=$$\frac{10}{2}$$

r=5

surface area of each ball=$$4\times \pi\times r^2$$

=$$4\times \pi\times 5^2$$

=$$4\times 25\times \pi$$

=$$100\pi$$

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