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.
Draw a picture of a horizontal slice through the silo and barn (a birds-eye view) It appears that the silo is intended to be a circular cylinder with a vertical slice removed, so your drawing will be of a circle with a cut across it. Mark the centre of the circle. Draw a line to the centre of the flat wall. Draw a radius to the part where the flat wall meets the curve on both sides, making two isoceles right angled triangles. You were given the two sides of the triangle, so you know the hypotenuse - this gives the radius of the circle. If you remove the two right angled triangles, you're left with the arc of a circle. Work out the area of the arc of the circle (do you see why it's 3/4 of a circle?). Add in the area of the two triangles. This gives the ara of the base, multiply by the height to get volume.
