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Question
If a cone and a sphere have equal radii and equal volumes. What is the ratio of the diameter of the sphere to the height of the cone?
Solution
Given that,
A cone and a sphere have equal radii and equal volume
i.e., volume of cone = volume of sphere
`1/3pi r_1^2 = 4/3 pir^3`
`r^2h = 4r^3`
`h = 4r^3`
`h = 4r`
`h = (2r) xx 2`
`h / 2r = 2/1`
`h/2 = 2/1` (diameterd = 2r)
`h : d = 2:1 or d: h = 1 : 2`
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