SOLUTION: A spherical balloon with radius r inches has a volume V(r)=4/3(pi)r(cubed). Find a function that represents the amount of air required to inflate the balloon from a radius of r in

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Question 395571: A spherical balloon with radius r inches has a volume V(r)=4/3(pi)r(cubed). Find a function that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r+1 inches.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A spherical balloon with radius r inches has a volume V(r)=4/3(pi)r(cubed).
Find a function that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r+1 inches.
:
Find the difference in their volumes
d(r) = %284%2F3%29%2Api%2A%28r%2B1%29%5E3 - %284%2F3%29%2Api%2Ar%5E3
:
Multiply (r+1)(r+1)(r+1)
d(r) = %284%2F3%29%2Api%2A%28r%5E3%2B3r%5E2%2B3r%2B1%29 - %284%2F3%29%2Api%2Ar%5E3
;
Factor out %284%2F3%29%2Api
d(r) = %284%2F3%29%2Api[r^3 + 3r^2 + 3r + 1 - r^3]
:
d(r) = %284%2F3%29%2Api[3r^2 + 3r + 1]; cu/in of air to be added