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A cone and a cylinder have their heights in the ratio 4: 5 and their diameters are in the ratio 3: 2. The ratio of their volumes will be
- a)5 : 3
- b)6 : 7
- c)3 : 5
- d)4 : 3
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A cone and a cylinder have their heights in the ratio 4: 5 and their d...
Explanation:
Given:
Height ratio of cone and cylinder = 4:5
Diameter ratio of cone and cylinder = 3:2
Volume of Cone:
The volume of a cone is given by the formula: V = (1/3)πr^2h
where r is the radius of the cone and h is the height of the cone.
Volume of Cylinder:
The volume of a cylinder is given by the formula: V = πr^2h
where r is the radius of the cylinder and h is the height of the cylinder.
Calculation:
Let the height of the cone be 4x and the height of the cylinder be 5x.
Let the diameter of the cone be 3y and the diameter of the cylinder be 2y.
Then, the radius of the cone (r) = 3y/2 and the radius of the cylinder (r) = 2y/2 = y.
Now, the volume of the cone = (1/3)π(3y/2)^2(4x) = (1/3)π(9y^2/4)(4x) = (3/4)πy^2x
The volume of the cylinder = π(y)^2(5x) = 5πy^2x
Therefore, the ratio of the volumes of the cone and the cylinder = (3/4)πy^2x : 5πy^2x
= 3/4 : 5
= 3 : 5
Therefore, the ratio of the volumes of the cone and the cylinder is 3:5.
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Community Answer
A cone and a cylinder have their heights in the ratio 4: 5 and their d...
Option C is correct
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A cone and a cylinder have their heights in the ratio 4: 5 and their diameters are in the ratio 3: 2. The ratio of their volumes will bea)5 : 3b)6 : 7c)3 : 5d)4 : 3Correct answer is option 'C'. Can you explain this answer?
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