SOLUTION: The area of a zone is 50.265 sq.cm. If the altitude of the zone is 2 cm, solve the surface area of the sphere.

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Question 1203309: The area of a zone is 50.265 sq.cm. If the altitude of the zone is 2 cm, solve the surface area of the sphere.
Answer by MathLover1(20849) About Me  (Show Source):
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Surface area of a sphere:
+A=4%2Api%2Ar%5E2
let altitude be +h+and diameter +d

given:
+h=2cm

The area of a spherical zone is +A=50.265cm%5E2

using the formula +A=2pi%2Arh where +h is the height of the spherical layer and +r is the radius of the sphere, substitute given

+50.265cm%5E2=2pi%2Ar%2A2cm ....solve for r
+r=50.265cm%5E2%2F%282pi%2A2cm%29.....simplify
+r=50.265cm%2F%284pi%29
+r=50.265cm%2F%284pi%29
+r=3.9999616072570596cm
+r=4cm

then, surface area of a sphere is:
+A=4%2Api%2A%284cm%29%5E2
+A=4%2Api%2A16cm%5E2
+A=64pi%2Acm%5E2
+A=201.062cm%5E2