Question

A rectangular piece of paper 44 cm long and 33 cm wide is made into cylindrical by rolling its long its width find the volume of the cylinder so formed

Answer 1

$\underline { \blue { Dimensions \: rectangular \: piece \: of \: paper : }}$

$Length (l) = 44 \: m ,\\Breadth (b) = 33\:cm$

/* According to the problem given*/

$If \: the \:paper \: rolled \: to \: make \: it \: a \\ cylinder$

$\underline { \blue { Dimensions \: of \: the \: cylinder: }}$

$Let \: the \: base \: radius = r \: cm$

$Circumference \: of \: circle (base)\\ = Length \: of \: the \: rectangular \:paper$

$\implies 2\pi r = l$

$\implies 2 \times \frac{22}{7} \times r = 44$

$\implies r = \frac{44 \times 7 }{ 2 \times 22}$

$\implies r = 7 \:cm$

$Height \: of \: the \: cylinder (h) = b = 33\:cm$

$\red { Volume \: of \: the \: Cylinder (V) } \\= \pi r^{2} h \\= \frac{22}{7} \times 7^{2} \times 33 \\= 22 \times 7 \times 33 \\= 5082 \: cm^{3}$

Therefore.,

$\red { Volume \: of \: the \: Cylinder (V) }\green {= 5082 \: cm^{3}}$

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