Question

A rectangular sheet of paper is rolled along its length to make a cylinder . The sheet is 33cm long and 32 cm wide. A circular sheet of paper is attached to bottom of the cylinder find capacity of cylinder
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Answer 1

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$\large{\underbrace{\sf{\green{Correct\:Question:}}}}$

A rectangular sheet of paper is rolled along its length to make a cylinder.the sheet is 33 cm long and 32 cm wide a circular sheet of paper is attached to the bottom of the cylinder formed.

Given :-

Length of the rectangular sheet = 33 cm.

Width of the rectangular sheet = 32 cm.

To Find:-

Capacity or volume of the cylinder.

Solution:-

✤ Length of the rectangular sheet = Circumference of the circle.

$\large\boxed{\underline{\red{\sf Circumference \: of \: the \: circle = 2\pi r}}}$

$\pink{\implies\:\:}$ ${\sf{ 33 \: cm = \dfrac{2 \times 22}{7 \times r} }}$

$\pink{\implies\:\:}$ ${\sf{ r = \dfrac{33 \times 7}{22 \times 2} }}$

$\pink{\implies\:\:}$ ${\sf{ r = \dfrac{231}{44} }}$

$\pink{\implies\:\:}$ ${\sf{ r = 5.25 \: cm }}$

${\boxed{{\sf{Capacity \: or \: volume \: of \: the \: cylinder = \pi {r}^{2} h}}}}$

$\purple{\implies\:\:}$ ${\sf{ \dfrac{22}{7 \times 5.25 \times 5.25 \times 32} }}$

$\purple{\implies\:\:}$ ${\sf{ \dfrac{22}{7 \times 27 .5625 \times 32} }}$

$\purple{\implies\:\:}$ ${\sf{ \dfrac{19404}{7} }}$

$\purple{\implies\:\:}$ ${\sf{ 2772 \: {cm}^{3} }}$

✤ Hence, the capacity or volume of the cylinder = 2772 cm³.

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