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

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) (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) = -
:
Multiply (r+1)(r+1)(r+1)
d(r) = -
;
Factor out
d(r) = [r^3 + 3r^2 + 3r + 1 - r^3]
:
d(r) = [3r^2 + 3r + 1]; cu/in of air to be added
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