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Sreepriya

Feb 24, 2015

A sphere ,cylinder and a cone of same radius and same height find the ratio of their CSA.

Raghunath Reddy

Since, the height of a sphere is the diameter, the cone and cylinder have height 2r.

Then

Curved surface area of Sphere= 4Ï€rÂ²

Curved surface area of cylinder = 2Ï€r(2r) = 4Ï€rÂ²

Curved surface area of cone = Ï€rl

where, l = âˆš(r^{2} + h^{2} ) = âˆš( r^{2} + (2r)^{2}) = âˆš(5r^{2}) = râˆš5

â‡’ Curved surface area of cone = Ï€âˆš5r^{2}

Now,

Ratio of CSA 's a sphere ,cylinder and a cone = 4Ï€r^{2}:2Ï€rh : Ï€rl

= 4Ï€r^{2}:4Ï€r^{2} : Ï€r^{2}âˆš5

= 4 : 4 : âˆš5

Parthasaradhi M

Member since Apr 1, 2017

Radhika

4r:2h:l