Question

Show that the surface area of a sphere is the same as that of LSA of a cylinder that just encloses the sphere

Answer 1

Step-by-step explanation:

SA of sphere= 4πr²

CSA of cylinder=2πrh

now as Cylinder just emcloses sphere, radius of sphere=radius of cylinder

also h=2r          ---------(1)

then take CSA and substitute values

cylinder=2πrh

             =2πr2r              [from (1)]

              =4πr²

hence proved

Answer 2

Answer:

SA of sphere= 4πr²

CSA of cylinder=2πrh

now as Cylinder just emcloses sphere, radius of sphere=radius of cylinder

also h=2r          ---------(1)

then take CSA and substitute values

cylinder=2πrh

            =2πr2r              [from (1)]

             =4πr²

THEREFORE PROVED