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Feb 24, 2015

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

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

Raghunath Reddy

Member since Apr 11, 2014

Since, the height of a sphere is the diameter, the cone and cylinder have height 2r.  Then  Curved surface area of Sphere= 4πr² Curved surface area of cylinder = 2πr(2r) = 4πr² Curved surface area of cone = πrl where, l = √(r2 + h2 ) = √( r2 + (2r)2) = √(5r2) = r√5   ⇒ Curved surface area of cone = π√5r2  Now,  Ratio of CSA 's a sphere ,cylinder and a cone = 4πr2:2πrh : πrl = 4πr2:4πr2 : πr2√5 = 4 : 4 : √5

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4r:2h:l
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