Question

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

• A. $3.03\%$
• B. $3.5\%$
• C. $4\%$
• D. $2.5\%$

Answer 1

Answer: (A)

$3.03\%$

Let the radius of the original cylinder $=r$ cm and height $=h$ cm
Original volume $=\pi r^{2}h$
New radius after increase $=1.01r$
New height after increase $=1.01h$
Now, new volume of the cylinder $=\pi \times {\left(1.01r\right)}^2\times \left(1.01h\right)=1.030301\pi r^{2}h$
% decrease $=\frac{\text{Change in volume}}{\text{Original volume}}\times 100$

$=\frac{1.030301\pi r^{2}h-\pi r^{2}h}{\pi r^{2}h}\times 100$

$=\frac{0.030301\pi r^{2}h}{\pi r^{2}h}\times 100$

$=3.0301\%$