Find the function that represents the amount of air required to fill a balloon from radius (r) to radius (r+1)?

Question

I already have the answer, but I'm having a hard time understanding the steps. Here they are: 
ΔV(r) = V(r+1)−V(r)
= 4/3π(r+1)^3 − 4/3πr^3
= 4/3π((r+1)3−r3) 
= 4π(3r^2+3r+1)

My problem is on this step:
= 4/3π(r+1)^3 − 4/3πr^3
= 4/3π((r+1)^3−r3) 

QUESTION: Where does the 4/3pi go?

? · Accepted Answer

V(r + 1) - V(r)

4pi/3 * (r + 1)^3 - 4pi/3 * r^3

Now take the 4pi/3 and multiply this by ((r + 1)^3 - r^3) in parentheses

= (4pi/3) * ((r+1)^3 - r^3)
= (4pi/3) * (r^3 + 3r^2 + 3r + 1 - r^3)
= (4pi/3) * (3r^2 + 3r + 1)

= 4pi(r^2 + r + 1/3)

The answer you reproduced in the question contains a number of errors.

Just Jess · Answer

Well to answer your question, it's the distributive property,

A * B + A * C = A * (B + C)
A = 4/3 pi
B = r+1^3
C = r^3

It's easy to miss the way it's written.

Trending News

Find the function that represents the amount of air required to fill a balloon from radius (r) to radius (r+1)?

2 Answers