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Asked by Sreepriya

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.

Answers(2)

Answer

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

Radhika

Member since

4r:2h:l
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