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the radio of two cylinder are in the ratio of 1: √3 if the volume of two cylinder be same , find the ratio of their respective height?
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Understanding the Problem
To find the ratio of the heights of two cylinders with equal volumes and given radii in the ratio of 1:√3, we start by recalling the formula for the volume of a cylinder.
Volume of a Cylinder
The volume (V) of a cylinder is given by the formula:
V = πr²h
where r is the radius and h is the height of the cylinder.
Given Conditions
- Let the radius of the first cylinder be r1 = 1.
- Let the radius of the second cylinder be r2 = √3.
- Both cylinders have the same volume, V.
Setting Up the Equations
Using the volume formula for both cylinders:
1. For the first cylinder:
- V1 = π(1)²h1 = πh1
2. For the second cylinder:
- V2 = π(√3)²h2 = 3πh2
Since the volumes are equal (V1 = V2), we set the equations equal to each other:
πh1 = 3πh2
Simplifying the Equation
By cancelling out π from both sides, we get:
h1 = 3h2
Finding the Ratio of Heights
To find the ratio of the heights, we can express h1 in terms of h2:
- h1/h2 = 3/1
Thus, the ratio of the heights of the two cylinders is:
Final Ratio
- The ratio of the heights of the two cylinders is 3:1.
This means the height of the first cylinder is three times that of the second cylinder.
To find the ratio of the heights of two cylinders with equal volumes and given radii in the ratio of 1:√3, we start by recalling the formula for the volume of a cylinder.
Volume of a Cylinder
The volume (V) of a cylinder is given by the formula:
V = πr²h
where r is the radius and h is the height of the cylinder.
Given Conditions
- Let the radius of the first cylinder be r1 = 1.
- Let the radius of the second cylinder be r2 = √3.
- Both cylinders have the same volume, V.
Setting Up the Equations
Using the volume formula for both cylinders:
1. For the first cylinder:
- V1 = π(1)²h1 = πh1
2. For the second cylinder:
- V2 = π(√3)²h2 = 3πh2
Since the volumes are equal (V1 = V2), we set the equations equal to each other:
πh1 = 3πh2
Simplifying the Equation
By cancelling out π from both sides, we get:
h1 = 3h2
Finding the Ratio of Heights
To find the ratio of the heights, we can express h1 in terms of h2:
- h1/h2 = 3/1
Thus, the ratio of the heights of the two cylinders is:
Final Ratio
- The ratio of the heights of the two cylinders is 3:1.
This means the height of the first cylinder is three times that of the second cylinder.
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?the radio of two cylinder are in the ratio of 1: √3 if the volume of two cylinder be same , find the ratio of their respective height?
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?the radio of two cylinder are in the ratio of 1: √3 if the volume of two cylinder be same , find the ratio of their respective height? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about ?the radio of two cylinder are in the ratio of 1: √3 if the volume of two cylinder be same , find the ratio of their respective height? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ?the radio of two cylinder are in the ratio of 1: √3 if the volume of two cylinder be same , find the ratio of their respective height?.
?the radio of two cylinder are in the ratio of 1: √3 if the volume of two cylinder be same , find the ratio of their respective height? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about ?the radio of two cylinder are in the ratio of 1: √3 if the volume of two cylinder be same , find the ratio of their respective height? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ?the radio of two cylinder are in the ratio of 1: √3 if the volume of two cylinder be same , find the ratio of their respective height?.
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