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Question
A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r, then the volume of the cylinder is
Options
4πr3
`8/3 pi r^3`
2πr3
8πr3
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Solution
In the given problem, we have a sphere inscribed in a cylinder such that it touches the top, base and the lateral surface of the cylinder. This means that the height and the diameter of the cylinder are equal to the diameter of the sphere.
So, if the radius of the sphere = r
The radius of the cylinder (rc)= r
The height of the cylinder (h) = 2r
Therefore, Volume of the cylinder = `pi r_c^2 h`
`= pi r^2 (2r) `
`=2 pi r^3`
So, the volume of the cylinder is `2 pi r^3` .
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