GATE2019 IN: GA-3

Question

The radius as well as the height of a circular cone increases by $10\%.$ The percentage increase in its  volume is ________.

• A. $17.1$
• B. $21.0$
• C. $33.1$
• D. $72.8$

Answer 1

Volume of a cone, $V = \frac{\pi}{3} r^2h$

$r \to 1.1r, h \to 1.1h \implies V \to 1.1^2 \times 1.1 V = 1.331 V$

So, percentage increase in volume $ = 33.1\%$

Correct Option: C

Comments

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

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

$\implies V = (1.1)^{2}\times 1.1 = (1.1)^{3} = 1.331 = (1.331-1)\times 100\% = 0.331\times 100\% = 33.1\%\Big \Uparrow$