A rectangular sheet of paper is rolled in two different ways to form two different cylinders. Find the volume of cylinders in each case if the sheet measures 44 cm × 33 cm.
Solution:
- A) Volume of the cylinder if it is rolled along the 44cm length is calculated below:
Volume = πr²h
Since the cylinder is formed by rolling along the 44cm length the circumference of the cylinder will be:
2πr = 33
2 × (22/7) × r = 33
r = 33 × (7/22) × 1/2
r = 3/4 × 7 = 21/4 = 5.25cm
Volume of the Cylinder = πr²h = (22/7) × (21/4)² × 44 = 3811.5cm³
B)Volume of the cylinder if it is rolled along the 33cm length is calculated below:
Volume = πr²h
Since the cylinder is formed by rolling along the 33cm length the circumference of the cylinder will be:
2πr = 44
2 × (22/7) × r = 44
r = 44 × (7/22) × 1/2
r = 7 cm
Volume of the Cylinder = πr²h = (22/7) × (7)² × 33 = 5082cm³
✦ Try This: A rectangular sheet of paper is rolled in two different ways to form two different cylinders. Find the volume of cylinders in each case if the sheet measures 22 cm × 11 cm.
- A) Volume of the cylinder if it is rolled along the 22cm length is calculated below:
Volume = πr²h
Since the cylinder is formed by rolling along the 22cm length the circumference of the cylinder will be:
2πr = 11
2 × (22/7) × r = 11
r = 7/4
r = 1.75cm
Volume of the Cylinder = πr²h = (22/7) × (7/4)² × 22 = 211.75.cm³
B)Volume of the cylinder if it is rolled along the 33cm length is calculated below:
Volume = πr²h
Since the cylinder is formed by rolling along the 11cm length the circumference of the cylinder will be:
2πr = 22
2 × (22/7) × r = 22
r = 7/2cm = 3.5cm
Volume of the Cylinder = πr²h = (22/7) × (7/2)² × 11 = 847/2 = 423.5cm³
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 126
A rectangular sheet of paper is rolled in two different ways to form two different cylinders. Find the volume of cylinders in each case if the sheet measures 44 cm × 33 cm.
Summary:
A rectangular sheet of paper is rolled in two different ways to form two different cylinders. The volume of cylinders in each case if the sheet measures 44 cm × 33 cm is 3811.5cm³ and 5082cm³
☛ Related Questions:
- A rectangular sheet of dimensions 25 cm × 7 cm is rotated about its longer side. Find the volume and . . . .
- From a pipe of inner radius 0.75 cm, water flows at the rate of 7 m per second. Find the volume in l . . . .
- Four times the area of the curved surface of a cylinder is equal to 6 times the sum of the areas of . . . .
visual curriculum