Question

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

• A. 1.01 p.c.
• B. 3.03 p.c.
• C. 2.01 p.c.
• D. 1.2 p.c.

Answer 1

Answer: (B)

3.03 p.c.

Let radius of penis cylinder is r and height of cylinder is h
$\therefore Volumeofcylinder=\pi r^{2}h$
New radius $=r+1$% or $r=r+\frac{1}{100}r=\frac{101}{100}r$
New height $h+1$% of $h=\frac{101}{100}h$
$\therefore$ Volume of new cylinder $=\pi {\left(\frac{101}{100}r\right)}^2\left(\frac{101}{100}h\right)=\frac{\pi (101{)}^3{r}^{2}h}{(100{)}^3}$\therefore$Increaseinvolume$= \displaystyle \left ( \frac{101}{100} \right )^3 r^2 h - \pi r^2 h= \pi (.030301) r^2 h$
Hence, percentage increase = 3.03 pc