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A right circular cylinder circumscribes ...

A right circular cylinder circumscribes a sphere of radius r. Find the ratio of the surface area of the sphere to the curved surface area of the cylinder.

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As cylinder circumscribes a sphere of radius `r`.
`:.` Height of cyllinder, `h = 2r`
Surface area of sphere `S_s = 4pir^2`
Surface area of cyllinder `S_c = 2pirh = 2pir(2r) = 4pir^2`
`:.` Ratio of the surface area of the sphere to the curved surface area of the cylinder `= S_s/S_c = (4pir^2)/(4pir^2) = 1/1`
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