SOLUTION: A design on the surface of a balloon is 5 cm wide when the balloon holds 71 cm^3 of air. How much air does the balloon hold when the design is 10 cm wide?

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Question 188907: A design on the surface of a balloon is 5 cm wide when the balloon holds 71 cm^3 of air. How much air does the balloon hold when the design is 10 cm wide?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A design on the surface of a balloon is 5 cm wide when the balloon holds 71 cm^3 of air.
How much air does the balloon hold when the design is 10 cm wide?
:
Let r = radius then balloon has 71 cu/cm
%284%2F3%29pi%2Ar%5E3 = 71
pi%2Ar%5E3 = 71+%2A+3%2F4
pi%2Ar%5E3 = 53.25
r^3 = 53.25%2Fpi
r^3 = 16.95
r = 2.57 cm when the balloon holds 71 cu/cm
:
Find the surface area:
SA = 4*pi*2.57^2
SA = 83 sq/cm
:
To double the surface area so the design goes from 5 cm to 10 cm wide
Find r for double the surface area
4*pi*r^2 = 166 sq/cm
r = sqrt%28166%2F%284%2Api%29%29
r = 3.63 cm
:
Find volume when r = 3.63
V = %284%2F3%29%2Api%2A3.63%5E3
V = 200.36 cu/cm