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If the radius of a cylinder is tripled and the height is halved, what is the ratio between the new volume and the previous volume?
- a)3:2
- b)4:5
- c)6:2
- d)9:2
Correct answer is option 'D'. Can you explain this answer?
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If the radius of a cylinder is tripled and the height is halved, what...
Let the initial radius and height of the cylinder be r cm and h cm respectively.
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Then, V1 = πr2 h and V2 = π.(3r).2.h/2 = 9/2 πr2h
New Volume/Previous Volume = 9/2πr2h/πr2h = 9/2 = 9:2
Most Upvoted Answer
If the radius of a cylinder is tripled and the height is halved, what...
To find the ratio between the new volume and the previous volume, we first need to calculate the volumes of the original and new cylinders.
Let's assume that the radius of the original cylinder is 'r' and the height is 'h'. Therefore, the volume of the original cylinder can be calculated using the formula:
Volume = πr^2h
Now, according to the given information, the radius of the new cylinder is tripled, which means the new radius is 3r. And the height is halved, which means the new height is h/2. Therefore, the volume of the new cylinder can be calculated using the same formula:
Volume = π(3r)^2(h/2) = π9r^2(h/2) = 9πr^2(h/2) = 9(πr^2h/2) = 9(Original Volume/2)
Therefore, the new volume is 9/2 times the original volume.
So, the ratio between the new volume and the previous volume is 9:2. Hence, the correct answer is option D.
Let's assume that the radius of the original cylinder is 'r' and the height is 'h'. Therefore, the volume of the original cylinder can be calculated using the formula:
Volume = πr^2h
Now, according to the given information, the radius of the new cylinder is tripled, which means the new radius is 3r. And the height is halved, which means the new height is h/2. Therefore, the volume of the new cylinder can be calculated using the same formula:
Volume = π(3r)^2(h/2) = π9r^2(h/2) = 9πr^2(h/2) = 9(πr^2h/2) = 9(Original Volume/2)
Therefore, the new volume is 9/2 times the original volume.
So, the ratio between the new volume and the previous volume is 9:2. Hence, the correct answer is option D.
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If the radius of a cylinder is tripled and the height is halved, what is the ratio between the new volume and the previous volume?a)3:2b)4:5c)6:2d)9:2Correct answer is option 'D'. Can you explain this answer?
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