Question

A square pool has volume 2,187 cubic feet and depth 9 feet. A couple builds a fence 3.5 feet high around the pool. How many square feet of fencing around the pool?

Answer 1

Answer:

Step-by-step explanation:

If the couple has build a fence around the pool we need to figure the perimeter around the top of the pool, because the fence is around the perimeter of the top of the pool.

So first they gave us the volume 2187 cubic feet, well we know the volume should be $V=lenght * width * depth$, if we plug that V is 2187 and and the depth is 9 we have $2187=lenght * width * 9$. Then dividing both sides by 9 we get the $243=lenght * width$. So see there we got the top area of the pool and since it says the pool is a squared pool then the top should be a square, remember in a square lenght is equal to width, because in a square all sides are the same. So instead of writing $243=lenght * width$ we can write $243=lenght^{2}$ , because remember in square the area is lenght squared.

Now if we take the square root at both sides in order to get rid of the lenght we have $\sqrt{243}=lenght$ then we use the calculator to figure the square root of 243 and we get that $15.58845727=lenght$.

So that is the side of the top of the pool. Now remember perimeter of a square is just side times 4, so in this case the perimeter is $4*15.58845727=62.35382907$

So there you have the perimeter around the pool we should cover, now in order to figure the amount of fence we should multiply that number we just got, that represents the base of the fence times the height of the fence which is 3.5

So the total area of fence is $3.5*62.35382907=218.2334018$

hope that helps, good bye :)