Two cylinders of equal volume have heights in the ratio 1:9. The ratio of their radii is __________.
Solution:
If height of one cylinder is h then the height of the second cylinder = 9h i.e.
h₁ = h
h₂ = 9h
h₁/h₂ = 1:9
Let r₁ = radius of first cylinder
Let r₂ = radius of second cylinder
If volume of cylinders 1 and 2 are same then we can write:
πr₁²h₁ = πr₂²h₂
r₁²/r₂² = h₂/h₁
r₁²/r₂² = 9/1 = 9
r₁/r₂ = √9
r₁/r₂ = 3
The ratio of the radii of the two cylinders will be 3:1.
✦ Try This: Two cylinders of equal volume have heights in the ratio 1:16. The ratio of their
radii is __________.
If height of one cylinder is h then the height of the second cylinder = 16h i.e.
h₁ = h
h₂ = 16h
h₁/h₂ = 1:16
Let r₁ = radius of first cylinder
Let r₂ = radius of second cylinder
If volume of cylinders 1 and 2 are same then we can write:
πr₁²h₁ = πr₂²h₂
r₁²/r₂² = h₂/h₁
r₁²/r₂² = 16/1 = 16
r₁/r₂ = √16
r₁/r₂ = 4
The ratio of the radii of the two cylinders will be 4:1.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 51
Two cylinders of equal volume have heights in the ratio 1:9. The ratio of their radii is __________
Summary:
Two cylinders of equal volume have heights in the ratio 1:9. The ratio of their radii is 3:1
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