Question

A spherical balloon with radius r inches has volume defined by the function below. 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 + 4 inches. (Give the answer in terms of π and r.)

Answer 1

The function is V(r+4) - V(r) = (4/3) pi (r+4)^3 - (3/4) pi r^3
= (4/3) pi ( (r+4)^3 -r^3)
=(4/3) pi ( r^3 + 12r^2 + 48r + 64 - r^3)
=(4/3) pi (12r^2 + 48r + 64)

Answer 2

Whoa I am a little confused!

Answer 3

(r+4)^3=r^3+12r^2+48r+64

Answer 4

The amount of air required is the volume of the balloon you want it to be given by V(r) subtract to the volume of the balloon to begin with given by V(r)

So
V(r+4) - V(r)

Answer 5

V(r+4)=(4/3) pi (r+4)^3
V(r)=(4/3) pi r^3

Answer 6

I am going to try to understand this and get back to you

Answer 7

Okay it's sort of in the steps I'd do because the highest common factor is (4/3) pi that's why it's outside the brackets