Expert: Steve Holleran - 12/12/2007

Question
a circular culvert has a radius of 30cm. the depth of water in the culvert is 45cm. what is the width of the water surface in the culvert? Round your answer to the nearest centimeter?

Answer
Hi Anna,

I hope I understand the setup of the question correctly.

In my diagram, I am looking at the circular cross-section of the culvert.  I drew a horizontal diameter,then went 15 cm up vertically from the center and drew another horizontal.  This is the width of the water surface, since it is 30 cm from the bottom to the center plus the 15 from the center making the 45 cm.

Then I drew a radius from the center to the right side point where the water surface meets the circumference of the culvert.  You should have a right triangle with hypotenuse 30 and the vertical leg 15.  Then by Pythagorean theorem, you have

               15^2 + x^2 = 30^2

and when I solved I got sqrt(675) = 25.9, so 26 cm would be half the width, which makes the width 52 cm.

Hope you can understand all this.
Steve