A sphere with radius 6 has two circular bands, each one unit wide when measured

Question

A sphere with radius 6 has two circular bands, each one unit wide when measured along the verticle height, painted about it. One band extends from a center circle to 1 unit above it, and the other from 3 units above the center circle to 4 units above. a) How much area is each band covering? b) How much area is the cap of the sphere covering from 5 units above the center to the top of the sphere? c) What can ou hypothesize about the area covered by each band with relation to where it lies on the sphere?

Explanation / Answer

area covering by first band=pi(1) area overing by another band=pi*(4^2-3^2)=21.98unit^2 b)area=pi*(6^2-5^2)=34.54 unit/62 c)it increases with increasing radius

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