The volume of a sphere:
r - the radius
The diameter is twice the radius.
![d=36 \ in \\ r=\frac{36}{2} \ in = 18 \ in \\ \\ V=\frac{4}{3} \pi \times 18^3=\frac{4}{3}\pi \times 5832=\frac{23328}{3} \pi=7776\pi \ [in^3]](https://tex.z-dn.net/?f=d%3D36%20%5C%20in%20%5C%5C%0Ar%3D%5Cfrac%7B36%7D%7B2%7D%20%5C%20in%20%3D%2018%20%5C%20in%20%5C%5C%20%5C%5C%0AV%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%5Ctimes%2018%5E3%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20%5Ctimes%205832%3D%5Cfrac%7B23328%7D%7B3%7D%20%5Cpi%3D7776%5Cpi%20%5C%20%5Bin%5E3%5D)
The exact volume of the sphere is 7776π in³.
So each of these statements are talking about the square footage of land per person. Let's go and find it!
First off, let's find the number in each building of the original complex:
280 people / 4 buildings
Each building has an equal number of residents. So just divide:
280/4 = 70.
So 70 residents per building
Now consider the fact that once a new building is built, another 70 people will move in.
280 + 70= 350
350 people total.
Then lets look at the plot of land
Originally, there are 200,000 square feet of land for the 4 buildings. Then after the expansion, the plot of land will be:
200,000 + 200*200
= 200,400
Go back to the question. What's the effect of the expansion in terms of square feet of land per person?
Divide!
200,400 / 350
Approximately = 572.57 square feet
Then since it's being compared to the amount each resident had before the expansion, do the same thing with the corresponding numbers:
200,000 / 280
Approximately = 714.29
So how much will each person's land decrease?
714.29 - 572.57 approximately = 141.72 square feet.
The answer is the first choice!
Hope this helps
