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Question
If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is
Options
2r
3r
r
4r
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Solution
In the given problem, we have a solid sphere which is remolded into a solid cone such that the radius of the sphere is equal to the height of the cone. We need to find the radius of the base of the cone.
Here, radius of the solid sphere (rs) = r cm
Height of the solid cone (h) = r cm
Let the radius of the base of cone (rc) = x cm
So, the volume of cone will be equal to the volume of the solid sphere.
Therefore, we get,
`(1/3) pi r_c^2 h = (4/3) pi r_s^3`
`(1/3) pi x^2 (r) = (4/3) pi (r)^3`
`x^2 = 4r^2`
` x = sqrt(4r^2)`
` x = 2r`
Therefore, radius of the base of the cone is 2r .
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