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A cylinder, a cone and a hemisphere are of equal base and have the same height. The ratio of their volumes is
- a)4: 5: 7
- b)3: 2: 1
- c)1: 2:3
- d)3: 1: 2
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A cylinder, a cone and a hemisphere are of equal base and have the sam...
According to me, Option D is not the right answer.....
option B is the right answer.
I am sorry because I couldn't able to attach the solution...
solution:
let r be the radius and h be the height.
so, ratio of volume of cylinder,cone& hemisphere=
πr²h: 1/3πr²h:2/3πr³
(since h=r)
=> πr³:1/3πr³:2/3πr³
=>1:1/3:2/3
=>3:1:2
your explanation.
option B is the right answer.
I am sorry because I couldn't able to attach the solution...
solution:
let r be the radius and h be the height.
so, ratio of volume of cylinder,cone& hemisphere=
πr²h: 1/3πr²h:2/3πr³
(since h=r)
=> πr³:1/3πr³:2/3πr³
=>1:1/3:2/3
=>3:1:2
your explanation.
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Community Answer
A cylinder, a cone and a hemisphere are of equal base and have the sam...
Explanation:
To solve this problem, we need to compare the volumes of a cylinder, a cone, and a hemisphere that have equal bases and heights.
Volume of a Cylinder:
The volume of a cylinder is given by the formula Vcylinder = πr^2h, where r is the radius of the base and h is the height.
Volume of a Cone:
The volume of a cone is given by the formula Vcone = (1/3)πr^2h, where r is the radius of the base and h is the height.
Volume of a Hemisphere:
The volume of a hemisphere is given by the formula Vhemisphere = (2/3)πr^3, where r is the radius of the base.
Since the bases of the three figures are equal, we can equate their radii.
Let:
r = radius of the base of each figure
h = height of each figure
Volume of the Cylinder:
Vcylinder = πr^2h
Volume of the Cone:
Vcone = (1/3)πr^2h
Volume of the Hemisphere:
Vhemisphere = (2/3)πr^3
Comparing the Volumes:
To find the ratio of the volumes, we divide each volume by the volume of the cylinder (Vcylinder). This will cancel out the common factor of πr^2h.
Ratio of Volumes:
Vcone/Vcylinder = (1/3)πr^2h / πr^2h = 1/3
Vhemisphere/Vcylinder = (2/3)πr^3 / πr^2h = 2rh/3rh = 2/3
Therefore, the ratio of the volumes of the cylinder, cone, and hemisphere is 1: 1/3: 2/3, which simplifies to 3: 1: 2.
Hence, the correct answer is option 'D' - 3: 2: 1.
To solve this problem, we need to compare the volumes of a cylinder, a cone, and a hemisphere that have equal bases and heights.
Volume of a Cylinder:
The volume of a cylinder is given by the formula Vcylinder = πr^2h, where r is the radius of the base and h is the height.
Volume of a Cone:
The volume of a cone is given by the formula Vcone = (1/3)πr^2h, where r is the radius of the base and h is the height.
Volume of a Hemisphere:
The volume of a hemisphere is given by the formula Vhemisphere = (2/3)πr^3, where r is the radius of the base.
Since the bases of the three figures are equal, we can equate their radii.
Let:
r = radius of the base of each figure
h = height of each figure
Volume of the Cylinder:
Vcylinder = πr^2h
Volume of the Cone:
Vcone = (1/3)πr^2h
Volume of the Hemisphere:
Vhemisphere = (2/3)πr^3
Comparing the Volumes:
To find the ratio of the volumes, we divide each volume by the volume of the cylinder (Vcylinder). This will cancel out the common factor of πr^2h.
Ratio of Volumes:
Vcone/Vcylinder = (1/3)πr^2h / πr^2h = 1/3
Vhemisphere/Vcylinder = (2/3)πr^3 / πr^2h = 2rh/3rh = 2/3
Therefore, the ratio of the volumes of the cylinder, cone, and hemisphere is 1: 1/3: 2/3, which simplifies to 3: 1: 2.
Hence, the correct answer is option 'D' - 3: 2: 1.
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A cylinder, a cone and a hemisphere are of equal base and have the same height. The ratio of their volumes isa)4: 5: 7b)3: 2: 1c)1: 2:3d)3: 1: 2Correct answer is option 'D'. Can you explain this answer?
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A cylinder, a cone and a hemisphere are of equal base and have the same height. The ratio of their volumes isa)4: 5: 7b)3: 2: 1c)1: 2:3d)3: 1: 2Correct answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A cylinder, a cone and a hemisphere are of equal base and have the same height. The ratio of their volumes isa)4: 5: 7b)3: 2: 1c)1: 2:3d)3: 1: 2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylinder, a cone and a hemisphere are of equal base and have the same height. The ratio of their volumes isa)4: 5: 7b)3: 2: 1c)1: 2:3d)3: 1: 2Correct answer is option 'D'. Can you explain this answer?.
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