Fred has installed a new swimming pool. The pool is shaped like a right hexagonal prism with a radius of 12 feet and a depth of 7 feet. They plan to have a pool party on the Fourth of July. If they begin filling the pool at noon on the first of July, will the pool be fully filled by noon on the Fourth? (necessary information: the hose filling the pool can produce 2 gallons of water every 30 seconds. To convert from cubic feet to gallons, you multiply by 7.48)



I got that the equation is 3*A*S where A is the apothem and S is the side... I got that it will only take 30 minutes to fill the pool and I know that is wrong... I've done it multiple times and I keep getting that. Is that right or am I wrong :confused: ? I also know that we had to find the apothem and had to use the 30-60-90 special triangles and I had 12 as the hypotenuse, 6 as the side length, and I got 10.39 as the apothem. HELP!!

I will show you this way. It is easy to follow.

If you draw a diagram of your pool you can see the hexagon is made up of 12 right triangles with angle 30 degrees. 360/12=30.

Now, as you probably know, the area of a right triangle is simply bh/2.



The area of each triangle is

There are 12 of these, so we have as the area of the hexagon.

But, it is 7 feet deep, so multiply by 7 and we get:

. Now, this is in cubic feet, not gallons.

To find gallons, as was stated, multiply by 7.48 and we get

gallons.

It is coming in at 4 gallons per minute.

That would be minutes to fill the pool.

That is hours or days to fill the pool.

It is 3 days from July 1 to July 4. But it takes 3.4 days to fill it. No.. it will not be full.

Fred will need 9.6 more hours. He should start filling it at around July 1st at 2 am if he

wants it filled by noon the 4th.