A sphere ,a cylinder and a cone are of the same radius and same height

1.	A sphere ,a cylinder and a cone are of the same radius and same heights. first the ratio of their curved surface areas.
Answer» Since, the height of a sphere is the diameter, the cone and cylinder have height 2r. ThenCurved 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 'sa sphere ,cylinder and a cone = 4πr2:2πrh : πrl = 4πr2:4πr2: πr2√5 = 4 : 4 : √5

A sphere ,a cylinder and a cone are of the same radius and same heights. first the ratio of their curved surface areas.

Answer»

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

ThenCurved 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 'sa sphere ,cylinder and a cone = 4πr2:2πrh : πrl

= 4πr2:4πr2: πr2√5

= 4 : 4 : √5