Question

please give me the proof of this formula, Suface area of a hemisphere = 4πr²

Answer 1

hope this will help uu...




Some solved examples on surface area of sphere - hemisphere 

1) The radius of hemispherical balloon increase from 7 cm to 14 cm as air is being pumped into it. Find the ratios of the surface areas of the balloon in two cases.
Solution :
For 1st hemisphere, r = 7 cm 
TSA -1 = 3 π r2
⇒ = 3 x π x 72
TSA-1 3 π x 72 1
-------- = --------- = ---- 
TSA -2 3π x 142 4⇒ S1 : S2 = 1 : 4
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2) Show that the surface area of sphere is same as that of the lateral surface area of a cylinder that just encloses the sphere.
Solution :
Total surface area of sphere = 4 π r2 ------(1)
The radius and height of the cylinder that just encloses the sphere of radius r and 2r respectively.
∴ CSA of cylinder = 2 π r h
⇒ = 2 π r x 2r 
∴ CSA of cylinder = 4 π r2 ----(2)
∴ From (1) and (2) 
Surface area of sphere is same as that of the lateral surface area of a cylinder that just encloses the sphere.