Question 62

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 ball be $$r$$ cm and radius of solid sphere = $$R=10$$ cm

=> Volume of sphere = $$\frac{4}{3}\pi R^3$$

According to ques,

=> $$\frac{4}{3}\pi R^3=8\times\frac{4}{3}\pi r^3$$

=> $$(10)^3=8r^3$$

=> $$r^3=(\frac{10}{2})^3$$

=> $$r=5$$ cm

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

=> $$4\times \pi\times25=100\pi$$ $$cm^2$$

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