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 Question from Amy, a teacher: Without using the Pythagorean Theorem, determine the capacity of a silo in cubic feet of grain if: the cylinder-shaped silo has one flat, rectangular face that rests against the side of the barn; the height of the silo is 30 feet and the face resting against the barn is 10 feet wide; the barn is approximately 5 feet from the center of the silo.

Amy,

The volume of the silo is the area of the base times the height. I drew a diagram of the base that you described.

D is the midpoint of the side against the barn so triangle CDB is isosceles and angle CDB is a right angle. Thus

5/|BC| = sin(45o) = 1/√2

and hence

|BC| = 5 √2

Thus the radius of the silo is 5 √2 ft and angle BCA is a right angle.

Can you complete the problem from here?

Is this argument allowed? The theorem of Pythagoras is so pervasive in the geometry of circles and trigonometry I'm not actually sure if my argument is "without using the Pythagorean Theorem".

Harley

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.