Question

Question 126

A rectangular sheet of paper is rolled in two different ways to form two different cylinders. Find the volume of cylinders in each case if the sheet measures $44cm\times 33cm$

Answer 1

In 1st case,
If sheet rolled along 33 cm

$\Rightarrow 2\pi r=44cm$
$\therefore r=\frac{44}{2\pi }=\frac{44}{2}\times \frac{7}{22}=7cm$
In IInd case,
If sheet rolled along 44 cm

$\Rightarrow 2\pi r=33\therefore r=\frac{33}{2\pi }=\frac{33\times 7}{2\times 22}=\frac{3\times 7}{2\times 2}=\frac{21}{4}cm$
Volume in 1st case,
Volume of cylinder $=\pi \times r^2\times h=\frac{22}{7}\times 7\times 7\times 33$ [$\because$ r = 7 cm and h = 33 cm]
$=22\times 33\times 7=5082c{m}^3$
Volume in IInd case,
Volume of cylinder $=\pi r^{2}h=\frac{22}{7}\times \frac{21}{4}\times \frac{21}{4}\times 44$ $[\because r=\frac{21}{4}cm=44cm]$
$=\frac{22\times 3\times 21\times 11}{4}=3811.5c{m}^3$