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The radii of two cylinders of the same height are in the ratio 4 :5, then find the ratio of their volumes.?
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The radii of two cylinders of the same height are in the ratio 4 :5, t...
Solution:
Let's assume that the radii of the two cylinders are 4x and 5x (since the ratio between their radii is given as 4:5) and the height of both cylinders is h.
The volume of a cylinder is given by the formula:
V = πr²h
Where V is the volume, r is the radius, and h is the height.
Now, let's calculate the volume of the first cylinder with radius 4x:
V₁ = π(4x)²h
V₁ = 16πx²h
Similarly, the volume of the second cylinder with radius 5x is:
V₂ = π(5x)²h
V₂ = 25πx²h
Now, let's find the ratio of their volumes:
Ratio of volumes = V₁ / V₂
Ratio of volumes = (16πx²h) / (25πx²h)
We can cancel out the common terms in the numerator and denominator, such as "πx²h":
Ratio of volumes = 16 / 25
Therefore, the ratio of the volumes of the two cylinders is 16:25.
Conclusion:
The ratio of the volumes of two cylinders with radii in the ratio 4:5 is 16:25.
Let's assume that the radii of the two cylinders are 4x and 5x (since the ratio between their radii is given as 4:5) and the height of both cylinders is h.
The volume of a cylinder is given by the formula:
V = πr²h
Where V is the volume, r is the radius, and h is the height.
Now, let's calculate the volume of the first cylinder with radius 4x:
V₁ = π(4x)²h
V₁ = 16πx²h
Similarly, the volume of the second cylinder with radius 5x is:
V₂ = π(5x)²h
V₂ = 25πx²h
Now, let's find the ratio of their volumes:
Ratio of volumes = V₁ / V₂
Ratio of volumes = (16πx²h) / (25πx²h)
We can cancel out the common terms in the numerator and denominator, such as "πx²h":
Ratio of volumes = 16 / 25
Therefore, the ratio of the volumes of the two cylinders is 16:25.
Conclusion:
The ratio of the volumes of two cylinders with radii in the ratio 4:5 is 16:25.
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The radii of two cylinders of the same height are in the ratio 4 :5, then find the ratio of their volumes.?
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The radii of two cylinders of the same height are in the ratio 4 :5, then find the ratio of their volumes.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The radii of two cylinders of the same height are in the ratio 4 :5, then find the ratio of their volumes.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radii of two cylinders of the same height are in the ratio 4 :5, then find the ratio of their volumes.?.
The radii of two cylinders of the same height are in the ratio 4 :5, then find the ratio of their volumes.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The radii of two cylinders of the same height are in the ratio 4 :5, then find the ratio of their volumes.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radii of two cylinders of the same height are in the ratio 4 :5, then find the ratio of their volumes.?.
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