Question 117

If the radius of sphere is decreased by 10%, then by what percent volume of sphere will decrease?

Solution

Let radius of sphere = $$r=10$$ cm

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

Let $$\frac{4}{3} \pi=k$$ (constant)

=> $$V=1000k$$ $$cm^3$$

After decreasing the radius by 10%, new radius = $$r'=10-(\frac{10}{100}\times10)$$

= $$10-1=9$$ cm

=> New volume = $$V'=(9)^3k=729k$$ $$cm^3$$

$$\therefore$$ Decrease in volume = $$\frac{(1000-729)}{1000}\times100$$

= $$\frac{271}{10}=27.1\%$$

=> Ans - (B)

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