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The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius √3 is
- a)4π
- b)4/3√3π
- c)8/3√3π
- d)2π
Correct answer is option 'A'. Can you explain this answer?
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The volume of the largest possible right circular cylinder that can b...
To find the volume of the largest possible right circular cylinder inscribed in a sphere, we need to understand the relationship between the cylinder and the sphere.
- The largest possible cylinder that can be inscribed in a sphere will have its height equal to the diameter of the sphere. This is because the diameter of the sphere is the maximum distance between any two points on the sphere, and the cylinder's height should be equal to this distance to maximize its volume.
- The cylinder will also have its base lying on the equator of the sphere. This ensures that the cylinder's base has the maximum possible area, resulting in a larger volume.
Let's calculate the volume of the cylinder using the given information:
- The diameter of the sphere is √3 times the radius of the sphere. Since the radius of the sphere is √3, the diameter is 2√3.
- Therefore, the height of the cylinder is equal to the diameter of the sphere, which is 2√3.
Using the formula for the volume of a cylinder, which is V = πr^2h, where r is the radius of the cylinder and h is the height, we can calculate the volume as follows:
- The radius of the cylinder is equal to half the diameter, which is √3/2.
- Substituting the values into the formula, we have V = π(√3/2)^2 * 2√3.
- Simplifying this expression, we get V = π(3/4) * 2√3.
- Further simplifying, V = (3/2)π√3.
Comparing this with the given options, we see that the correct answer is option 'A', which is 4π.
- The largest possible cylinder that can be inscribed in a sphere will have its height equal to the diameter of the sphere. This is because the diameter of the sphere is the maximum distance between any two points on the sphere, and the cylinder's height should be equal to this distance to maximize its volume.
- The cylinder will also have its base lying on the equator of the sphere. This ensures that the cylinder's base has the maximum possible area, resulting in a larger volume.
Let's calculate the volume of the cylinder using the given information:
- The diameter of the sphere is √3 times the radius of the sphere. Since the radius of the sphere is √3, the diameter is 2√3.
- Therefore, the height of the cylinder is equal to the diameter of the sphere, which is 2√3.
Using the formula for the volume of a cylinder, which is V = πr^2h, where r is the radius of the cylinder and h is the height, we can calculate the volume as follows:
- The radius of the cylinder is equal to half the diameter, which is √3/2.
- Substituting the values into the formula, we have V = π(√3/2)^2 * 2√3.
- Simplifying this expression, we get V = π(3/4) * 2√3.
- Further simplifying, V = (3/2)π√3.
Comparing this with the given options, we see that the correct answer is option 'A', which is 4π.
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Community Answer
The volume of the largest possible right circular cylinder that can b...
Let r be the radius of the cylinder and 2h be the height.
Also 
⇒ h = 1
Vmax = 2π(3 − 1) = 4π.
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The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius √3 isa)4πb)4/3√3πc)8/3√3πd)2πCorrect answer is option 'A'. Can you explain this answer?
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