Question

2. (8 points) A zone of a sphere is the portion of its surface which lies between two parallel planes which intersect the sphere. The altitude of the zone is the distance between the planes. Show that the surface area A of a zone depends only on its altitude h and the radius R of the sphere. [hint: you need to express A as a function of h and R.]

Answer 1

Yardig there is a side view. The sphere can be formed by rotating the circle with radius R around the we are looking in a direction parallel to Paines at yua at y = a and y= ath. The Zone they are talking about is the Surbace formed by the part of the carce between the planes, rotated about the y-cais -D athy - R O akty p² REFREY & CR2_x)" (***) => da 11 dy -Y. > = dy (R2 y 23 2 we know that by JuJet du du are length (21)

ནི། it lady d writing an integral to represent the Lone ath S= 21 ) dy a ath ling dy R²y² = 20 12² R?_y? dy R²-42 zar( ath-a) 1+ y² ith ath = 20 1 pa dy S zakh depends which represente Sou are alreau only on is altitude and the radius ob the sphere.