A spherical balloon with radius r inches has volume V(r) = 4/3 πr^3. 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 πr^3.  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.)

anonymous · Answer

i am new to this this site any help will be appreciated

anonymous · Answer

Before you add the extra air the volume is$$V_1=\frac{ 4 }{ 3 }\pi r^3$$After you add the extra air the volume is$$V_2=\frac{ 4 }{ 3 }\pi (r+3)^3$$Your answer is V2 - V1. To make it pretty you should multiply out (r+3)^3. One of the terms will be r^3, so when you subtract V1 you'll get something without any r^3 term.