Two cylinders A and B are formed by folding a rectangular sheet of dimensions 20 cm × 10 cm along its length and also along its breadth respectively. Then volume of A is ________ of volume of B.
Solution:
Since cylinder A is rolled along the length of the rectangular sheet and will form a cylinder of circumference of 20 cm.
2πr = 20 cm
r = 10/π
Since volume(V) = πr²h
V(A) = π(10/π)²h
Now h = 10 cm
V(A) = (100/π) × 10 = 1000/π
The cylinder B is formed along the breadth of 10 cm
2πr = 10 cm
r = 5/π
Since volume(V) = πr²h
V(B) = π(5/π)²h
Now h = 20 cm
V(B) = (25/π) × 20 = 500/π
V(A)/V(B) = [1000/π]/[500/π] = 2
Volume of cylinder A is twice the volume of cylinder B.
✦ Try This: Cylinders A is formed by folding a rectangular sheet of dimensions 20 cm × 10 cm along its length and cylinder B by folding a rectangular sheet of dimensions 20 cm × 20 cm along its length. Then the volume of A is ________ of volume of B.
Cylinder A:
2πr = 20 cm
2 × (π) × r = 20
r = 10/π
Therefore The volume cylinders will be:
Volume(V) = πr²h = (π) × (10/π) × (10/π) × 10
Where height h = 10 cm
V = 1000/π cm³
Cylinder B:
2πr = 20 cm
2 × (π) × r = 20
r = 10/π
h = 20 cm
Therefore The volume cylinders will be:
Volume(V) = πr²h = (π) × (10/π) × (10/π) × 20
V = 2000/π
The Volume of cylinder A will then become half of Volume B.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 47
Two cylinders A and B are formed by folding a rectangular sheet of dimensions 20 cm × 10 cm along its length and also along its breadth respectively. Then volume of A is ________ of volume of B.
Summary:
Two cylinders A and B are formed by folding a rectangular sheet of dimensions 20 cm × 10 cm along its length and also along its breadth respectively. Then volume of A is twice that of volume of B
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