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If the radius of a right circular cone is increased by $50\%$ its volume increases by

  1. $75\%$
  2. $100\%$
  3. $125\%$
  4. $237.5\%$
in Numerical Ability by Boss (17.2k points)
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Volume of  the cone $V=\frac{1}{3}\pi r^{2}h$

Here only radius change so we can write $V\propto r^{2}$

$r\rightarrow r+\frac{50}{100}r \implies r\rightarrow 1.5r$

New volume $ {V}'\propto (1.5r)^{2} \propto 2.25r^{2}$

Percentage changes in volume $=\frac{2.25r^{2}-r^{2}}{r^{2}}\times 100=1.25\times 100=125\%$

So, correct option is $(C)$
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