11. A rectangular sheet of paper 72 cm x 48 cm is rolled along its length and
a cylinder is formed. Find the volume of the cylinder.
Answers
Given :
- Length of the rectangular sheet = 72 cm
- Breadth of the rectangular sheet = 48 cm
- The rectangular sheet is rolled along its length and a cylinder is formed.
To find :
- Volume of the cylinder
Concept Used :
→ Formula of circumference of cylinder :-
- Circumference = 2πr
→ Formula of volume of cylinder :-
- Volume of cylinder = πr²h
where,
- Take π = 22/7
- r = radius
- h = height
As the rectangular sheet is rolled along its length and a cylinder is formed. So, the length of the rectangular sheet will be equal to the circumference of the cylinder and the breadth of the rectangular sheet will be equal to height of the cylinder.
So, by using the formula of circumference we will find the radius and then by substituting the values in the formula of volume of cylinder we will get our required answer.
Solution :
Length of the sheet = Circumference of cylinder
∴ Circumference of cylinder = 72 cm
Using formula,
• Circumference = 2πr
Substituting the given values,
⇒ 72 = 2 × 22/7 × r
⇒ 72 = 44/7 × r
⇒ 72 × 7/44 = r
⇒ 36 × 7/22 = r
⇒ 18 × 7/11 = r
⇒ 126/11 = r
⇒ 11.45 = r
Radius of the cylinder = 126/11 cm or 11.45 cm
Breadth of the sheet = Height of the cylinder
∴ Height of the cylinder = 48 cm
Using formula,
• Volume of cylinder = πr²h
Substituting the given values,
⇒ Volume = 22/7 × 11.45 × 11.45 × 48
⇒ Volume = 19,777.75
★ Volume of the cylinder = 19,777.75 cm³