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A cone, hemisphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes.?
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A cone, hemisphere and a cylinder stand on equal bases and have the sa...
Ratio of Volumes of Cone, Hemisphere, and Cylinder
The cone, hemisphere, and cylinder all stand on equal bases and have the same height. Let's determine the ratio of their volumes.
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.
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.
Calculating the Ratio
Since the cone, hemisphere, and cylinder have the same height, we can cancel out the height from the volume formulas.
Ratio of Volumes:
Vcone : Vhemisphere : Vcylinder
= (1/3)πr^2h : (2/3)πr^3 : πr^2h
= 1 : 2r : 3
Therefore, the ratio of the volumes of the cone, hemisphere, and cylinder is 1 : 2r : 3.
The cone, hemisphere, and cylinder all stand on equal bases and have the same height. Let's determine the ratio of their volumes.
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.
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.
Calculating the Ratio
Since the cone, hemisphere, and cylinder have the same height, we can cancel out the height from the volume formulas.
Ratio of Volumes:
Vcone : Vhemisphere : Vcylinder
= (1/3)πr^2h : (2/3)πr^3 : πr^2h
= 1 : 2r : 3
Therefore, the ratio of the volumes of the cone, hemisphere, and cylinder is 1 : 2r : 3.
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A cone, hemisphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes.?
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A cone, hemisphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes.? 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 cone, hemisphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cone, hemisphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes.?.
A cone, hemisphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes.? 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 cone, hemisphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cone, hemisphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes.?.
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