Question

If a solid right circular cylinder made of iron is heated to increase its radius and height by $1$ percent each, then the volume of the solid is increased by

• A. $1.01\%$
• B. $3.03\%$
• C. $2.03\%$
• D. $1.2\%$

Answer 1

The correct option is B $3.03\%$

Let initial radius and height of cylinder be 'r' and 'h' respectively

Initial volume, $V_1=\pi r^{2}h$

New radius$=r+1$ % of r$=1.01r$

New height$=h+1$% of $1.01h$

New volume,$V_2=\pi {\left(1.01r\right)}^2\times 1.01h=1.0303\pi r^{2}h$

% increase in volume$=\frac{(1.0303-1)\pi r^{2}h}{\pi r^{2}h}\times 100=3.03$%