Question 59

If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball is

Solution

Let radius of each small spherical ball = $$r$$ cm

Volume of a sphere = $$\frac{4}{3}\pi r^3$$

=> $$8\times\frac{4}{3}\pi (r)^3=\frac{4}{3}\pi (10)^3$$

=> $$r^3=\frac{(10)^3}{8}$$

=> $$r=\frac{10}{2}=5$$

$$\therefore$$ Surface area of each ball = $$4\pi r^2$$

= $$4\times\pi \times(5)^2=100\pi$$ $$cm^2$$

=> Ans - (D)

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