OpenStudy (anonymous):

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.)

6 years ago
OpenStudy (anonymous):
6 years ago

OpenStudy (anonymous):

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)

6 years ago
OpenStudy (anonymous):

Whoa I am a little confused!

6 years ago
OpenStudy (anonymous):

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

6 years ago
OpenStudy (anonymous):

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)

6 years ago
OpenStudy (anonymous):

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

6 years ago
OpenStudy (anonymous):

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

6 years ago
OpenStudy (anonymous):

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

6 years ago