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The radii of two right circular cylinders are in the ratio 2: 3 and their heights are in the ratio 5: 4. The ratio of their volumes will be
  • a)
    4: 3
  • b)
    6: 7
  • c)
    5: 9
  • d)
    2: 3
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The radii of two right circular cylinders are in the ratio 2: 3 and th...
Ratio of Radii:
Let the radii of the two cylinders be 2x and 3x.

Ratio of Heights:
Let the heights of the two cylinders be 5y and 4y.

Volume of a Cylinder:
The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.

Finding the Volumes:
The volume of the first cylinder with radius 2x and height 5y is V₁ = π(2x)²(5y) = 20πx²y.
The volume of the second cylinder with radius 3x and height 4y is V₂ = π(3x)²(4y) = 36πx²y.

Ratio of Volumes:
The ratio of the volumes of the two cylinders is given by V₁ : V₂.
Substituting the values, we get V₁ : V₂ = 20πx²y : 36πx²y.
Simplifying, we get V₁ : V₂ = 5x²y : 9x²y.
Dividing both sides by x²y, we get V₁ : V₂ = 5 : 9.

Therefore, the ratio of the volumes of the two cylinders is 5 : 9, which corresponds to option C.
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The radii of two right circular cylinders are in the ratio 2: 3 and their heights are in the ratio 5: 4. The ratio of their volumes will bea)4: 3b)6: 7c)5: 9d)2: 3Correct answer is option 'C'. Can you explain this answer?
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