Expert: Paul Klarreich - 4/29/2006

Question
Hi,

 I have an interesting, and challenging word problem for you that I cannot seem to figure out.  Here it goes:

I am trying to find the volume of a swimming pool that is shaped like a perfect right triangle (82ft. x 82ft. x 116ft).  The depth by the hypotenuse is zero ft.  The depth gradually slopes downward at an equal rate ending with a depth at the right angle of 5ft.  I need to find the volume of the pool.

Thank you so much! i appreciate it!

Answer
Hi, Lindsay,

Your Question:  Hi,

I have an interesting, and challenging word problem for you that I cannot seem to figure out. Here it goes:

I am trying to find the volume of a swimming pool that is shaped like a perfect right triangle (82ft. x 82ft. x 116ft).

>> I assume you mean an isosceles right triangle.

The depth by the hypotenuse is zero ft.

>> Just like mine!  Now I know why it says 'no diving at this end.'

The depth gradually slopes downward at an equal rate ending with a depth at the right angle of 5ft. I need to find the volume of the pool.

Thank you so much! i appreciate it!
---------------------------
What you have is effectively a 'pyramid.'  Definition:

A pyramid has a base which is a polygon, and the top vertex is connected to each of the vertices of the base.

The volume of a pyramid, like a cone, which is a pyramid with an infinite number of sides, is  1/3 base * height.

So your 'base' is the triangle, which has area  1/2 82^2,  and the height is the 5-foot depth.  [Remember, 'base' for a geometric figure has nothing to do with top or bottom.]

So I think your volume is (1/3) (1/2) 82^2 (5)