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

Answer 1

Given : 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 
Given : 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 

Answer 2

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

• 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.