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The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. What is the ratio of their volumes?
- a)20 : 27
- b)27 : 20
- c)9 : 4
- d)4 : 9
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The radii of two cylinders are in the ratio 2 : 3 and their heights ar...
Given:
The ratio of the radii of two cylinders is 2:3.
The ratio of the heights of the two cylinders is 5:3.
To find:
The ratio of their volumes.
Solution:
Let's assume the radii of the cylinders to be 2x and 3x, and the heights to be 5y and 3y respectively.
Volume of a cylinder:
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Volume of the first cylinder:
V1 = π(2x)^2(5y)
V1 = 4πx^2y
Volume of the second cylinder:
V2 = π(3x)^2(3y)
V2 = 9πx^2y
Ratio of their volumes:
V1 : V2 = (4πx^2y) : (9πx^2y)
V1 : V2 = 4x^2y : 9x^2y
Simplifying the ratio:
The common factors x^2 and y cancel out.
V1 : V2 = 4 : 9
Therefore, the ratio of the volumes of the two cylinders is 4:9, which is equivalent to 20:27.
Final Answer:
The ratio of the volumes of the two cylinders is 20:27. Hence, the correct option is (a) 20:27.
The ratio of the radii of two cylinders is 2:3.
The ratio of the heights of the two cylinders is 5:3.
To find:
The ratio of their volumes.
Solution:
Let's assume the radii of the cylinders to be 2x and 3x, and the heights to be 5y and 3y respectively.
Volume of a cylinder:
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Volume of the first cylinder:
V1 = π(2x)^2(5y)
V1 = 4πx^2y
Volume of the second cylinder:
V2 = π(3x)^2(3y)
V2 = 9πx^2y
Ratio of their volumes:
V1 : V2 = (4πx^2y) : (9πx^2y)
V1 : V2 = 4x^2y : 9x^2y
Simplifying the ratio:
The common factors x^2 and y cancel out.
V1 : V2 = 4 : 9
Therefore, the ratio of the volumes of the two cylinders is 4:9, which is equivalent to 20:27.
Final Answer:
The ratio of the volumes of the two cylinders is 20:27. Hence, the correct option is (a) 20:27.
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Community Answer
The radii of two cylinders are in the ratio 2 : 3 and their heights ar...
Let the radii of two cylinders are 2r, 3r and heights be 5h and 3h.
Ratio of their volumes
Ratio of their volumes
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The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. What is the ratio of their volumes?a)20 : 27b)27 : 20c)9 : 4d)4 : 9Correct answer is option 'A'. Can you explain this answer?
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