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If the radius of the base of a right circular cylinder is halved keeping the height same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is
- a)1:2
- b)2:1
- c)4:1
- d)1:4
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If the radius of the base of a right circular cylinder is halved keepi...
You know the formula for vol. Of a cylinder is pi*r^2*h And when radius is halved, the vol. will be changed to pi* (r/2)^2*h =pi*(r^2)/4*h... This is 1/4th of the former vol., so the required ratio of their vol.s is 1:4
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If the radius of the base of a right circular cylinder is halved keepi...
Explanation:
To understand the ratio of the volumes of the original and the new cylinder, let's consider the formulas for the volume of a cylinder.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height.
Let's assume the original cylinder has a radius r and height h.
1. The volume of the original cylinder is V1 = πr^2h.
2. If the radius of the base is halved, the new radius becomes r/2, but the height remains the same.
3. The volume of the new cylinder is V2 = π(r/2)^2h = π(r^2/4)h = (π/4)r^2h.
Calculating the Ratio:
To find the ratio of the volumes, we can divide the volume of the new cylinder by the volume of the original cylinder.
Ratio = V2/V1 = [(π/4)r^2h] / [πr^2h]
Simplifying the expression:
Ratio = (π/4)r^2h / πr^2h
The πr^2h terms cancel out:
Ratio = 1/4
Therefore, the ratio of the volume of the cylinder with halved radius to the volume of the original cylinder is 1:4, or option D.
Conclusion:
When the radius of the base of a right circular cylinder is halved while keeping the height the same, the volume of the new cylinder becomes one-fourth the volume of the original cylinder.
To understand the ratio of the volumes of the original and the new cylinder, let's consider the formulas for the volume of a cylinder.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height.
Let's assume the original cylinder has a radius r and height h.
1. The volume of the original cylinder is V1 = πr^2h.
2. If the radius of the base is halved, the new radius becomes r/2, but the height remains the same.
3. The volume of the new cylinder is V2 = π(r/2)^2h = π(r^2/4)h = (π/4)r^2h.
Calculating the Ratio:
To find the ratio of the volumes, we can divide the volume of the new cylinder by the volume of the original cylinder.
Ratio = V2/V1 = [(π/4)r^2h] / [πr^2h]
Simplifying the expression:
Ratio = (π/4)r^2h / πr^2h
The πr^2h terms cancel out:
Ratio = 1/4
Therefore, the ratio of the volume of the cylinder with halved radius to the volume of the original cylinder is 1:4, or option D.
Conclusion:
When the radius of the base of a right circular cylinder is halved while keeping the height the same, the volume of the new cylinder becomes one-fourth the volume of the original cylinder.
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If the radius of the base of a right circular cylinder is halved keeping the height same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder isa)1:2b)2:1c)4:1d)1:4Correct answer is option 'D'. Can you explain this answer?
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