Question

The volume, V $c{m}^2$, of a hollow cylindrical pipe of length $l$ cm, outer radius R cm and inner radius r cm is given by the formula : $V=\pi (R^2-r^2).l$

Find r, if $V=22,R=2,l=4$ and $\pi ,3\frac{1}{7}.$

• A. 1.5
• B. 1.2
• C. 1.4
• D. 1.6

Answer 1

Answer: (A)

1.5

Given $V=\pi (R^2-r^2)l$

$V=\pi R^2-\pi r^{2}l$

$\pi r^{2}l=\pi R^{2}l-V$

$r^2=\frac{\pi R^{2}l-V}{\pi l}$

$\therefore r=\sqrt{\frac{\pi R^{2}l-V}{\pi l}}$

Given $V=22,R=2,L=4,\pi =3\frac{1}{7}=\frac{22}{7}$

$\therefore r=\sqrt{\frac{\frac{22}{7}\times 4\times 4-22}{\frac{22}{7}\times 4}}=\sqrt{\frac{352-154}{88}}=\sqrt{\frac{198}{88}}=\sqrt{\frac{9}{4}}=1.5$