A spherical balloon with radius r inches has volume V(r) = 4 3 πr3. Find an expression that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r + 3 inches. (Express your answer in terms of π and r.)

Question

A spherical balloon with radius r inches has volume  V(r) =  4 3 πr3.  Find an expression that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r + 3 inches. (Express your answer in terms of π and r.)

goformit100 · Answer

First of all @bnblack : A Warm Welcome to 'Open Study'. Please Read CoC (compulsory to read by all "Open Study" users) : http://openstudy.com/code-of-conduct

anonymous · Answer

you want to find the change in volume:

V = V(r+3) - V(r)

anonymous · Answer

Okay thank you very much!

anonymous · Answer

V(r) is already given. To find V(r+3) plug (r+3) instead of r in V(r)

$$V(r+3)=\frac{ 4 }{ 3 }π(r+3)^3$$

let me know if you need help expanding (r+3)^3

anonymous · Answer

glad i could help :)