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Volume of cylinder - class-IX
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The volume, V $cm^{2}$, 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 $\pi,, 3\displaystyle \frac{1}{7}.$
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A
1.5
💡 Explanation:
Given $V= \pi \left ( R^{2}-r^{2} \right )l$
$V= \pi R^{2}-\pi r^{2} l$
$\pi r^{2}l= \pi R^{2}l-V$
$ r^{2}= \dfrac{\pi R^{2}l-V}{\pi l}$
$\pi r^{2}l= \pi R^{2}l-V$
$ r^{2}= \dfrac{\pi R^{2}l-V}{\pi l}$
$\therefore r= \sqrt{\dfrac{\pi R^{2}l-V}{\pi l}}$
Given $V=22 ,R=2 ,L=4 , \pi = 3\tfrac{1}{7}= \frac{22}{7}$
$\therefore r= \sqrt{\dfrac{\frac{22}{7}\times 4\times 4-22}{\dfrac{22}{7}\times4}}= \sqrt{\dfrac{352-154}{88}}= \sqrt{\dfrac{198}{88}}= \sqrt{\dfrac{9}{4}}= 1.5$