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A cylindrical container is to be made from certain solid material with the following constraints: It has a
fixed inner volume of V mm3, has a 2 mm thick solid wall and is open at the top. The bottom of the
container is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of the
container.
If the volume of the material used to make the container is minimum when the inner radius of the container
is 10 mm, then the value of V/250π is
fixed inner volume of V mm3, has a 2 mm thick solid wall and is open at the top. The bottom of the
container is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of the
container.
If the volume of the material used to make the container is minimum when the inner radius of the container
is 10 mm, then the value of V/250π is
Correct answer is '4'. Can you explain this answer?
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To find the value of V/250, we first need to find the height of the cylindrical container.
The inner radius of the container is given as 10 mm. The outer radius of the container is the inner radius plus the thickness of the wall, which is 2 mm. So, the outer radius is 12 mm.
The bottom of the container is a solid circular disc with a thickness of 2 mm and a radius of 12 mm. The volume of this disc is given by V_disc = π * r^2 * h, where r is the radius and h is the thickness. Plugging in the values, we get V_disc = π * 12^2 * 2 = 288π mm^3.
The inner volume of the container is fixed at V mm^3. We need to subtract the volume of the disc from the inner volume to find the volume of the cylindrical part of the container. So, the volume of the cylinder is V_cylinder = V - V_disc = V - 288π mm^3.
The volume of a cylinder is given by V_cylinder = π * r^2 * h, where r is the radius and h is the height. Plugging in the values, we get V - 288π = π * 10^2 * h.
Simplifying the equation, we get V - 288π = 100πh.
To find the minimum value of V, we need to minimize the value of h. To do that, we differentiate the equation with respect to h and set it equal to zero.
d/dh[V - 288π] = d/dh[100πh]
0 = 100π
0 = π
Since this is a contradiction, we cannot find the minimum value of V by differentiating the equation.
Therefore, it is not possible to determine the value of V/250 with the given information.
The inner radius of the container is given as 10 mm. The outer radius of the container is the inner radius plus the thickness of the wall, which is 2 mm. So, the outer radius is 12 mm.
The bottom of the container is a solid circular disc with a thickness of 2 mm and a radius of 12 mm. The volume of this disc is given by V_disc = π * r^2 * h, where r is the radius and h is the thickness. Plugging in the values, we get V_disc = π * 12^2 * 2 = 288π mm^3.
The inner volume of the container is fixed at V mm^3. We need to subtract the volume of the disc from the inner volume to find the volume of the cylindrical part of the container. So, the volume of the cylinder is V_cylinder = V - V_disc = V - 288π mm^3.
The volume of a cylinder is given by V_cylinder = π * r^2 * h, where r is the radius and h is the height. Plugging in the values, we get V - 288π = π * 10^2 * h.
Simplifying the equation, we get V - 288π = 100πh.
To find the minimum value of V, we need to minimize the value of h. To do that, we differentiate the equation with respect to h and set it equal to zero.
d/dh[V - 288π] = d/dh[100πh]
0 = 100π
0 = π
Since this is a contradiction, we cannot find the minimum value of V by differentiating the equation.
Therefore, it is not possible to determine the value of V/250 with the given information.
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A cylindrical container is to be made from certain solid material with the following constraints: It has afixed inner volume of V mm3, has a 2 mm thick solid wall and is open at the top. The bottom of thecontainer is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of thecontainer.If the volume of the material used to make the container is minimum when the inner radius of the containeris 10 mm, then the value of V/250π isCorrect answer is '4'. Can you explain this answer?
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A cylindrical container is to be made from certain solid material with the following constraints: It has afixed inner volume of V mm3, has a 2 mm thick solid wall and is open at the top. The bottom of thecontainer is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of thecontainer.If the volume of the material used to make the container is minimum when the inner radius of the containeris 10 mm, then the value of V/250π isCorrect answer is '4'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A cylindrical container is to be made from certain solid material with the following constraints: It has afixed inner volume of V mm3, has a 2 mm thick solid wall and is open at the top. The bottom of thecontainer is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of thecontainer.If the volume of the material used to make the container is minimum when the inner radius of the containeris 10 mm, then the value of V/250π isCorrect answer is '4'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical container is to be made from certain solid material with the following constraints: It has afixed inner volume of V mm3, has a 2 mm thick solid wall and is open at the top. The bottom of thecontainer is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of thecontainer.If the volume of the material used to make the container is minimum when the inner radius of the containeris 10 mm, then the value of V/250π isCorrect answer is '4'. Can you explain this answer?.
A cylindrical container is to be made from certain solid material with the following constraints: It has afixed inner volume of V mm3, has a 2 mm thick solid wall and is open at the top. The bottom of thecontainer is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of thecontainer.If the volume of the material used to make the container is minimum when the inner radius of the containeris 10 mm, then the value of V/250π isCorrect answer is '4'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A cylindrical container is to be made from certain solid material with the following constraints: It has afixed inner volume of V mm3, has a 2 mm thick solid wall and is open at the top. The bottom of thecontainer is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of thecontainer.If the volume of the material used to make the container is minimum when the inner radius of the containeris 10 mm, then the value of V/250π isCorrect answer is '4'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical container is to be made from certain solid material with the following constraints: It has afixed inner volume of V mm3, has a 2 mm thick solid wall and is open at the top. The bottom of thecontainer is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of thecontainer.If the volume of the material used to make the container is minimum when the inner radius of the containeris 10 mm, then the value of V/250π isCorrect answer is '4'. Can you explain this answer?.
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A cylindrical container is to be made from certain solid material with the following constraints: It has afixed inner volume of V mm3, has a 2 mm thick solid wall and is open at the top. The bottom of thecontainer is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of thecontainer.If the volume of the material used to make the container is minimum when the inner radius of the containeris 10 mm, then the value of V/250π isCorrect answer is '4'. Can you explain this answer?, a detailed solution for A cylindrical container is to be made from certain solid material with the following constraints: It has afixed inner volume of V mm3, has a 2 mm thick solid wall and is open at the top. The bottom of thecontainer is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of thecontainer.If the volume of the material used to make the container is minimum when the inner radius of the containeris 10 mm, then the value of V/250π isCorrect answer is '4'. Can you explain this answer? has been provided alongside types of A cylindrical container is to be made from certain solid material with the following constraints: It has afixed inner volume of V mm3, has a 2 mm thick solid wall and is open at the top. The bottom of thecontainer is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of thecontainer.If the volume of the material used to make the container is minimum when the inner radius of the containeris 10 mm, then the value of V/250π isCorrect answer is '4'. Can you explain this answer? theory, EduRev gives you an
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