Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In th...

Question

Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is

A. pi/3  B. 2pi/3  C. pi  D. 3pi

Accepted Answer

Volume of cone = pi/3 cubic units A unit square cut along the diagonal gives a right isosceles triangle with legs of length 1 each and hypotenuse sqrt(2). When one such triangle is revolved about one of its legs (the short edge), the leg becomes the axis of rotation. The other leg sweeps out the base circle, and the hypotenuse sweeps out the lateral surface. The cone has height equal to the axis leg and base radius equal to the perpendicular leg.