Question

A rectangular paper of width 14 cm is rolled along its width and a cylinder of radius 20 cm is formed find its volume

Answer 1

The length (l) and breadth (b) of the rectangular sheet are 44 cm and 20 cm



Now the sheet is rolled along the length to form cylinder.

Let the redius of the cylinder be r.

Then height (h) = b = 20 cm

and circumference = 44 cm

⇒ 2πr = 44 cm

⇒ r = 7 cm

Hence volume of cylinder formed = πr2h

= 3080 cm3

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Answer 2

$\huge \sf \underline \red{Answer : }$

$\sf \underline \purple{ \therefore \: Volume \: of \: cylinder = 17600 {cm}^{3}}$

$\huge \sf \underline \blue{To \: find : }$

• Volume = ?

$\huge \sf \underline \green{Solution : }$

$\sf \underline{Given : }$

• A rectangle paper is rolled along its width to form a cylinder

$\sf \underline{height \: of \: cylinder = width \: of \: rectangle = 14cm}$

$\sf \underline{h = 14cm}$

$\sf {Given}\begin{cases}&\sf{radius \: of \: cylinder = \sf{20cm}} \\ \\ &\sf{height \: of \: cylinder = \sf{14cm}} \ \: \}\end{cases}$

$⇢\sf \underline{We \: know \: that : }$

$\: \: \: \: \: \: \: \: \: \sf{ \boxed{ \underline{ \underline{ \red{ \sf{Volume \: of \: cylinder = \pi{r}^{2}h \: }}}}}}$

• Radius = 20cm

• Height = 14cm

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf⇢{\pi \times {(20)}^{2} \times 14}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf⇢{ \dfrac{22}{7} \times {(20)}^{2} \times 14}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf⇢{ \dfrac{22}{7} \times 20 \times 20 \times 14}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf⇢{22 \times 20 \times 20 \times 2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf⇢{44 \times 400}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf⇢{44 \times 4\times 100}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf⇢{176 \times 100}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf⇢{17600 {cm}^{3}}$

$\sf \underline \purple{ \therefore \: Volume \: of \: cylinder = 17600 {cm}^{3}}$