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Question
The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is
Options
2 : 1
1 : 1
2 : 3
1 : 2
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Solution
In the given problem, we need to find the ratio between the volume of a sphere and volume of a circumscribing right circular cylinder. This means that the diameter of the sphere and the cylinder are the same. Let us take the diameter as d.
Here,
Volume of a sphere (V1) = `(4/3) pi (d/2)^3`
`(4/3) pi (d^3/8)`
`= (pi d^3 ) /6`
As the cylinder is circumscribing the height of the cylinder will also be equal to the height of the sphere. So,
Volume of a cylinder (V2) = `pi (d/2)^2 h`
`= pi d^2/4(d)`
`=(pi d^3)/4`
Now, the ratio of the volume of sphere to the volume of the cylinder = `V_1/V_2`
`V_1/V_2=(((pid^3)/6))/(((pi d^3)/4))`
`=4/6`
`=2/3`
So, the ratio of the volume of sphere to the volume of the cylinder is 2: 3 .
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