# GATE2017 CE-1: GA-4

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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. $237.5\%$

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Migrated from GO Civil 1 year ago by Arjun

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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$V = \dfrac{1}{3}\pi r^{2}h$

$\implies V \propto r^{2}$

$\implies V = (1.5)^{2} = 2.25 = (2.25-1)\times 100\% = 1.25\times 100\% = 125\%\Big\Uparrow$

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