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A closed container is in the shape of a right circular cone of height h metre with some amount of water in it. when it is seen, such that it's vertex points downwards, it contain the water to height h/2 metre. Find the height( in terms of h) to which the same amount of water reach when, it is placed on it's circular base.?
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Problem Statement: A closed container is in the shape of a right circular cone of height h metre with some amount of water in it. When it is seen, such that its vertex points downwards, it contains the water to height h/2 metre. Find the height (in terms of h) to which the same amount of water reaches when it is placed on its circular base.
Solution:
Given, a right circular cone of height h and some amount of water in it. Let us assume the radius of the base of the cone is R.
When it is seen such that its vertex points downwards, it contains the water to height h/2 metre. This means that the volume of water in the cone is equal to half of the volume of the cone.
Let V be the volume of the cone and V' be the volume of water in the cone.
Then, V' = V/2
The volume of a cone is given by the formula:
V = (1/3)πR²h
Substituting V' = V/2, we get:
(1/3)πR²(h/2) = V/2
Simplifying the above equation, we get:
R² = h²/4
Therefore, R = h/2
Height to which the same amount of water reaches when the cone is placed on its circular base:
When the cone is placed on its circular base, the water in it will reach a certain height. Let us assume this height is h1.
The volume of the cone is the same as the volume of water in it. Therefore, we can equate the volume of the cone to the volume of water in it when it is placed on its circular base.
The volume of a cone is given by the formula:
V = (1/3)πR²h1
Substituting R = h/2, we get:
V = (1/3)π(h/2)²h1
Simplifying the above equation, we get:
V = (1/12)πh³
Substituting V' = V/2, we get:
(1/6)πh³ = (1/3)πR²(h/2)
Substituting R = h/2, we get:
(1/6)πh³ = (1/12)πh³(h/2)²
Simplifying the above equation, we get:
h1 = h/√3
Therefore, the height to which the same amount of water reaches when the cone is placed on its circular base is h/√3.
Solution:
Given, a right circular cone of height h and some amount of water in it. Let us assume the radius of the base of the cone is R.
When it is seen such that its vertex points downwards, it contains the water to height h/2 metre. This means that the volume of water in the cone is equal to half of the volume of the cone.
Let V be the volume of the cone and V' be the volume of water in the cone.
Then, V' = V/2
The volume of a cone is given by the formula:
V = (1/3)πR²h
Substituting V' = V/2, we get:
(1/3)πR²(h/2) = V/2
Simplifying the above equation, we get:
R² = h²/4
Therefore, R = h/2
Height to which the same amount of water reaches when the cone is placed on its circular base:
When the cone is placed on its circular base, the water in it will reach a certain height. Let us assume this height is h1.
The volume of the cone is the same as the volume of water in it. Therefore, we can equate the volume of the cone to the volume of water in it when it is placed on its circular base.
The volume of a cone is given by the formula:
V = (1/3)πR²h1
Substituting R = h/2, we get:
V = (1/3)π(h/2)²h1
Simplifying the above equation, we get:
V = (1/12)πh³
Substituting V' = V/2, we get:
(1/6)πh³ = (1/3)πR²(h/2)
Substituting R = h/2, we get:
(1/6)πh³ = (1/12)πh³(h/2)²
Simplifying the above equation, we get:
h1 = h/√3
Therefore, the height to which the same amount of water reaches when the cone is placed on its circular base is h/√3.
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A closed container is in the shape of a right circular cone of height h metre with some amount of water in it. when it is seen, such that it's vertex points downwards, it contain the water to height h/2 metre. Find the height( in terms of h) to which the same amount of water reach when, it is placed on it's circular base.?
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A closed container is in the shape of a right circular cone of height h metre with some amount of water in it. when it is seen, such that it's vertex points downwards, it contain the water to height h/2 metre. Find the height( in terms of h) to which the same amount of water reach when, it is placed on it's circular base.? 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 closed container is in the shape of a right circular cone of height h metre with some amount of water in it. when it is seen, such that it's vertex points downwards, it contain the water to height h/2 metre. Find the height( in terms of h) to which the same amount of water reach when, it is placed on it's circular base.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A closed container is in the shape of a right circular cone of height h metre with some amount of water in it. when it is seen, such that it's vertex points downwards, it contain the water to height h/2 metre. Find the height( in terms of h) to which the same amount of water reach when, it is placed on it's circular base.?.
A closed container is in the shape of a right circular cone of height h metre with some amount of water in it. when it is seen, such that it's vertex points downwards, it contain the water to height h/2 metre. Find the height( in terms of h) to which the same amount of water reach when, it is placed on it's circular base.? 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 closed container is in the shape of a right circular cone of height h metre with some amount of water in it. when it is seen, such that it's vertex points downwards, it contain the water to height h/2 metre. Find the height( in terms of h) to which the same amount of water reach when, it is placed on it's circular base.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A closed container is in the shape of a right circular cone of height h metre with some amount of water in it. when it is seen, such that it's vertex points downwards, it contain the water to height h/2 metre. Find the height( in terms of h) to which the same amount of water reach when, it is placed on it's circular base.?.
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