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Two identical right circular cones each of height 2 centimetre are placed vertically as shown in diagram at the start the perkins full of water and lower cone is empty then Water drips town through a hole in the effects of the par Kaun into the lower cone the height of the water in the lower cone at the moment and height of water in upper cone is one centimetre is?
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Two identical right circular cones each of height 2 centimetre are pla...
Let R be the radius of the base of each come and H (H=2) the total height.
When the height of water in the top cone is 1, the radius of the free surface is r and we must have r/R=1/H so r=R/H. The volume of water that left the top cone is therefore V = (1/3) pi R^2 H - (1/3) (R/H)^2 1 or
V=(1/3) pi R^2 (H^3-1)/H^2
If at that time the height of the water in the lower cone is h, then the radius of the free surface is hR/H and therefore the volume of water is (1/3) pi (hR/H)^2 h = (1/3) pi R^2 h^3/H^2
Equating the two obtained volumes we see that h^3 = H^3 - 1 = 2^3 - 1 = 7 so h is the cube root of 7 and therefore the correct answer is (D)
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Two identical right circular cones each of height 2 centimetre are pla...
Diagram:
The diagram shows two identical right circular cones placed vertically. The upper cone is filled with water and the lower cone is empty. The water drips down through a hole in the apex of the upper cone and fills the lower cone.
Given Information:
- Both cones have a height of 2 centimeters.
- Initially, the upper cone is filled with water up to a height of 1 centimeter.
Objective:
To determine the height of the water in the lower cone when the height of water in the upper cone is 1 centimeter.
Solution:
To solve this problem, we will use similar triangles and the concept of volumes of cones.
Step 1: Identifying Similar Triangles
Since the two cones are identical, the triangles formed by the height of the water and the radii of the cones are similar. Let's call the height of the water in the lower cone h (which we need to find) and the radius of the lower cone r.
Step 2: Setting up Proportions
Using the similar triangles, we can set up the following proportion:
(Height of water in upper cone)/(Height of water in lower cone) = (Radius of upper cone)/(Radius of lower cone)
Plugging in the given values, we have:
1 cm/h cm = r cm/r cm
Simplifying the proportion, we get:
1/h = 1/r
Step 3: Finding the Radius of the Lower Cone
Since the height of the water in the lower cone is h and the total height of the lower cone is 2 cm, we can use the proportion:
h/2 = r/2
Simplifying, we get:
h = r
Step 4: Determining the Height of the Water in the Lower Cone
Substituting the value of h in the proportion 1/h = 1/r, we have:
1/h = 1/h
This means that the height of the water in the lower cone is equal to the radius of the lower cone.
Conclusion:
Therefore, the height of the water in the lower cone when the height of water in the upper cone is 1 centimeter is also 1 centimeter.
The diagram shows two identical right circular cones placed vertically. The upper cone is filled with water and the lower cone is empty. The water drips down through a hole in the apex of the upper cone and fills the lower cone.
Given Information:
- Both cones have a height of 2 centimeters.
- Initially, the upper cone is filled with water up to a height of 1 centimeter.
Objective:
To determine the height of the water in the lower cone when the height of water in the upper cone is 1 centimeter.
Solution:
To solve this problem, we will use similar triangles and the concept of volumes of cones.
Step 1: Identifying Similar Triangles
Since the two cones are identical, the triangles formed by the height of the water and the radii of the cones are similar. Let's call the height of the water in the lower cone h (which we need to find) and the radius of the lower cone r.
Step 2: Setting up Proportions
Using the similar triangles, we can set up the following proportion:
(Height of water in upper cone)/(Height of water in lower cone) = (Radius of upper cone)/(Radius of lower cone)
Plugging in the given values, we have:
1 cm/h cm = r cm/r cm
Simplifying the proportion, we get:
1/h = 1/r
Step 3: Finding the Radius of the Lower Cone
Since the height of the water in the lower cone is h and the total height of the lower cone is 2 cm, we can use the proportion:
h/2 = r/2
Simplifying, we get:
h = r
Step 4: Determining the Height of the Water in the Lower Cone
Substituting the value of h in the proportion 1/h = 1/r, we have:
1/h = 1/h
This means that the height of the water in the lower cone is equal to the radius of the lower cone.
Conclusion:
Therefore, the height of the water in the lower cone when the height of water in the upper cone is 1 centimeter is also 1 centimeter.
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Two identical right circular cones each of height 2 centimetre are placed vertically as shown in diagram at the start the perkins full of water and lower cone is empty then Water drips town through a hole in the effects of the par Kaun into the lower cone the height of the water in the lower cone at the moment and height of water in upper cone is one centimetre is?
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Two identical right circular cones each of height 2 centimetre are placed vertically as shown in diagram at the start the perkins full of water and lower cone is empty then Water drips town through a hole in the effects of the par Kaun into the lower cone the height of the water in the lower cone at the moment and height of water in upper cone is one centimetre is? 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 Two identical right circular cones each of height 2 centimetre are placed vertically as shown in diagram at the start the perkins full of water and lower cone is empty then Water drips town through a hole in the effects of the par Kaun into the lower cone the height of the water in the lower cone at the moment and height of water in upper cone is one centimetre is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical right circular cones each of height 2 centimetre are placed vertically as shown in diagram at the start the perkins full of water and lower cone is empty then Water drips town through a hole in the effects of the par Kaun into the lower cone the height of the water in the lower cone at the moment and height of water in upper cone is one centimetre is?.
Two identical right circular cones each of height 2 centimetre are placed vertically as shown in diagram at the start the perkins full of water and lower cone is empty then Water drips town through a hole in the effects of the par Kaun into the lower cone the height of the water in the lower cone at the moment and height of water in upper cone is one centimetre is? 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 Two identical right circular cones each of height 2 centimetre are placed vertically as shown in diagram at the start the perkins full of water and lower cone is empty then Water drips town through a hole in the effects of the par Kaun into the lower cone the height of the water in the lower cone at the moment and height of water in upper cone is one centimetre is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two identical right circular cones each of height 2 centimetre are placed vertically as shown in diagram at the start the perkins full of water and lower cone is empty then Water drips town through a hole in the effects of the par Kaun into the lower cone the height of the water in the lower cone at the moment and height of water in upper cone is one centimetre is?.
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