Two cylinders of the same volume have their radii in the ratio 1:6, then the ratio of their heights is __________.
Solution:
If height of one cylinder is h then the height of the second cylinder = 16h i.e.
Let h₁ = height of cylinder 1
Let h₂ = height of cylinder 2
Let r₁ = radius of first cylinder
Let r₂ = radius of second cylinder
r₁/r₂ = 1:6
r₁²/r₂² = (1/6)² = 1/36
If the volume of cylinders 1 and 2 are same then we can write:
πr₁²h₁ = πr₂²h₂
r₁²/r₂² = h₂/h₁
h₂/h₁ = r₁²/r₂² = 1/36
Therefore
h₁/h₂ = 36:1
The ratio of the heights of the two cylinders will be 36:1.
✦ Try This: Two cylinders of same volume have their radii in the ratio 1:4, then ratio of their heights is _________.
If height of one cylinder is h then the height of the second cylinder = 16h i.e.
Let h₁ = height of cylinder 1
Let h₂ = height of cylinder 2
Let r₁ = radius of first cylinder
Let r₂ = radius of second cylinder
r₁/r₂ = 1:4
r₁²/r₂² = (1/6)² = 1/16
If the volume of cylinders 1 and 2 are same then we can write:
πr₁²h₁ = πr₂²h₂
r₁²/r₂² = h₂/h₁
h₂/h₁ = r₁²/r₂² = 1/16
Therefore
h₁/h₂ = 16:1
The ratio of the heights of the two cylinders will be 36:1.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 52
Two cylinders of the same volume have their radii in the ratio 1:6, then the ratio of their heights is __________.
Summary:
Two cylinders of same volume have their radii in the ratio 1:6, then ratio of their heights is 36:1
☛ Related Questions:
visual curriculum