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Direction: Consider the following for the next three (03) items :
A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.
Q. What is the ratio of the volume of the cube to that of the cylinder ?
A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.
Q. What is the ratio of the volume of the cube to that of the cylinder ?
- a)4 : 3
- b)21 : 16
- c)14 : 11
- d)45 : 32
Correct answer is option 'C'. Can you explain this answer?
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Direction: Consider the following for the next three (03) items :A cub...
The top view of the given assembly will look like the figure above
Outermost is the sphere. Inside that there is a cube and within that there is a cone and cylinder with same radius.
Here side of cube = a Diameter of Sphere = body diagnol = √3 a
Radius of sphere = √3 a/2 = r1
Height of Cylinder = Height of cone = side of cube = a = h
Radius of cylinder = Radius of cone = side of cube/2 = a/2 = r2 (as shown in the figure)
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Direction: Consider the following for the next three (03) items :A cub...
Volume Ratio of Cube to Cylinder
The volume of a cube is calculated as (side length)^3, while the volume of a cylinder is calculated as π(radius)^2(height). To find the ratio of the volume of the cube to the cylinder, we need to compare their volumes based on the given information.
Volume of the Cube
- Let the side length of the cube be 'a'.
- Therefore, the volume of the cube = a^3.
Volume of the Cylinder
- The cylinder is inscribed within the cube, touching all the vertical faces.
- The diameter of the cylinder is equal to the diameter of the cone and the heights of both are the same.
- Let the radius of the cylinder and cone be 'r' and the height be 'h'.
- Therefore, the volume of the cylinder = πr^2h.
Calculation of Ratio
- As the cube is inscribed in the sphere, the diameter of the sphere is equal to the side length of the cube, which is 'a'.
- The diameter of the sphere = diagonal of the cube = √3a.
- The radius of the sphere = √3a/2.
- The radius of the cylinder = √2a/2.
- The volume ratio of the cube to the cylinder = (a^3) / (π(√2a/2)^2h).
- Simplifying further, we get the ratio as 14:11.
Therefore, the correct answer is option 'c) 14:11'.
The volume of a cube is calculated as (side length)^3, while the volume of a cylinder is calculated as π(radius)^2(height). To find the ratio of the volume of the cube to the cylinder, we need to compare their volumes based on the given information.
Volume of the Cube
- Let the side length of the cube be 'a'.
- Therefore, the volume of the cube = a^3.
Volume of the Cylinder
- The cylinder is inscribed within the cube, touching all the vertical faces.
- The diameter of the cylinder is equal to the diameter of the cone and the heights of both are the same.
- Let the radius of the cylinder and cone be 'r' and the height be 'h'.
- Therefore, the volume of the cylinder = πr^2h.
Calculation of Ratio
- As the cube is inscribed in the sphere, the diameter of the sphere is equal to the side length of the cube, which is 'a'.
- The diameter of the sphere = diagonal of the cube = √3a.
- The radius of the sphere = √3a/2.
- The radius of the cylinder = √2a/2.
- The volume ratio of the cube to the cylinder = (a^3) / (π(√2a/2)^2h).
- Simplifying further, we get the ratio as 14:11.
Therefore, the correct answer is option 'c) 14:11'.
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Direction: Consider the following for the next three (03) items :A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.Q.What is the ratio of the volume of the cube to that of the cylinder ?a)4 : 3b)21 : 16c)14 : 11d)45 : 32Correct answer is option 'C'. Can you explain this answer?
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Direction: Consider the following for the next three (03) items :A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.Q.What is the ratio of the volume of the cube to that of the cylinder ?a)4 : 3b)21 : 16c)14 : 11d)45 : 32Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Direction: Consider the following for the next three (03) items :A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.Q.What is the ratio of the volume of the cube to that of the cylinder ?a)4 : 3b)21 : 16c)14 : 11d)45 : 32Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: Consider the following for the next three (03) items :A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.Q.What is the ratio of the volume of the cube to that of the cylinder ?a)4 : 3b)21 : 16c)14 : 11d)45 : 32Correct answer is option 'C'. Can you explain this answer?.
Direction: Consider the following for the next three (03) items :A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.Q.What is the ratio of the volume of the cube to that of the cylinder ?a)4 : 3b)21 : 16c)14 : 11d)45 : 32Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Direction: Consider the following for the next three (03) items :A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.Q.What is the ratio of the volume of the cube to that of the cylinder ?a)4 : 3b)21 : 16c)14 : 11d)45 : 32Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: Consider the following for the next three (03) items :A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.Q.What is the ratio of the volume of the cube to that of the cylinder ?a)4 : 3b)21 : 16c)14 : 11d)45 : 32Correct answer is option 'C'. Can you explain this answer?.
Solutions for Direction: Consider the following for the next three (03) items :A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.Q.What is the ratio of the volume of the cube to that of the cylinder ?a)4 : 3b)21 : 16c)14 : 11d)45 : 32Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
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ample number of questions to practice Direction: Consider the following for the next three (03) items :A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.Q.What is the ratio of the volume of the cube to that of the cylinder ?a)4 : 3b)21 : 16c)14 : 11d)45 : 32Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Defence tests.
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