Question

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

• A. $1.01\%$
• B. $3.03\%$
• C. $2.01\%$
• D. $1.2\%$

Answer 1

Answer: (B)

$3.03\%$

Let radius of cylinder is $r$ and height of cylinder is $h$
$\therefore$ volume of cylinder $=\pi r^{2}h$
New radius $=r+1$% of $r=r+\frac{1}{100}r=\frac{101}{100}r$
New height $=h+1$% of $h=\frac{101}{100}h$
$\therefore$ Volume of new cylinder $=\pi {\left(\frac{101}{100}r\right)}^2\left(\frac{101}{100}h\right)$
$=\frac{(101{)}^3{r}^{2}h}{(100{)}^3}$
$\therefore$ Increase in volume $={\left(\frac{101}{100}\right)}^3{r}^{2}h-\pi r^{2}h$
$=\pi \left(0.030301\right)r^{2}h$
Hence, percentage increase $=$ $3.03\%$