Answer:
x + 3
Step-by-step explanation:
To solve this we are going to use the formula for the volume of a sphere:
![V= \frac{4}{3} \pi r^3](https://tex.z-dn.net/?f=V%3D%20%5Cfrac%7B4%7D%7B3%7D%20%20%5Cpi%20r%5E3)
where
![r](https://tex.z-dn.net/?f=r)
is the radius of the sphere
Remember that the radius of a sphere is half its diameter; since the first radius of our sphere is 24 cm,
![r= \frac{24}{2} =12](https://tex.z-dn.net/?f=r%3D%20%5Cfrac%7B24%7D%7B2%7D%20%3D12)
. Lets replace that in our formula:
![V= \frac{4}{3} \pi r^3](https://tex.z-dn.net/?f=V%3D%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E3)
![V= \frac{4}{3} \pi (12)^3](https://tex.z-dn.net/?f=V%3D%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%2812%29%5E3)
![V=7238.23 cm^3](https://tex.z-dn.net/?f=V%3D7238.23%20cm%5E3)
Now, the second diameter of our sphere is 36, so its radius will be:
![r= \frac{36}{2} =18](https://tex.z-dn.net/?f=r%3D%20%5Cfrac%7B36%7D%7B2%7D%20%3D18)
. Lets replace that value in our formula one more time:
![V= \frac{4}{3} \pi r^3](https://tex.z-dn.net/?f=V%3D%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E3)
![V= \frac{4}{3} \pi (18)^3](https://tex.z-dn.net/?f=V%3D%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%2818%29%5E3)
![V=24429.02](https://tex.z-dn.net/?f=V%3D24429.02)
To find the volume of the additional helium, we are going to subtract the volumes:
Volume of helium=
![24429.02cm^3-7238.23cm^3=17190.79cm^3](https://tex.z-dn.net/?f=24429.02cm%5E3-7238.23cm%5E3%3D17190.79cm%5E3)
We can conclude that the volume of additional helium in the balloon is
approximately <span>
17,194 cm³.</span>
Answer:
2(r+4)(r-4)
Step-by-step explanation
First, you want to factor out 2 from both terms, which gives you 2(r^2-16). Then you want to recognize that (r^2-16) is factorable into 2 terms. If you multiply (r+4) by (r-4) then you are given (r^2-16) as a result.
I think 10 sweaters and 55 dollars left over. :)