Question 121

If the radius of a sphere is increased by 2 cm, then its surface area increases by 352 $$cm^2$$. The radius of the sphere initially was: (use $$\pi=\frac{22}{7}$$)

Solution

Let initial radius = $$r$$ cm

Initial surface area = $$4\pi r^2$$

New radius = $$(r+2)$$ cm

=> New surface area = $$4\pi (r+2)^2=4\pi r^2+352$$

=> $$4\pi r^2+16\pi r+16\pi=4\pi r^2+352$$

=> $$16\pi(r+1)=352$$

=> $$(r+1)=\frac{352}{16}\times\frac{7}{22}$$

=> $$(r+1)=7$$

=> $$r=7-1=6$$ cm

=> Ans - (C)

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