SolidsProducedbyRotatingPolygons

　　The question asks you to figure out the surface area of the cone. The formula for surface area is πr2 + πrl, which means you need to know the lateral height of the cone and the radius of the circle. If you’ve drawn your cone correctly, you should see that the lateral height is equal to the hypotenuse of the triangle. The radius of the circle is equal to side BC of the triangle. You can easily calculate the length of BC since the triangle is a 30-60-90 triangle. If the hypotenuse is 2, then BC, being the side opposite the 30o angle, must be 1. Now plug both values of l and r into the surface area formula and then simplify:

　　Common Rotations　　You don’t need to learn any new techniques or formulas for problems that deal with rotating figures. You just have to be able to visualize the rotation as it’s described and be aware of which parts of the polygons become which parts of the geometric solid. Below is a summary of which polygons, when rotated a specific way, produce which solids.

　　A rectangle rotated about its edge produces a cylinder.A semicircle rotated about its diameter produces a sphere.A right triangle rotated about one of its legs produces a cone.

　　A rectangle rotated about a central axis (which must contain the midpoints of both of the sides that it intersects) produces a cylinder.A circle rotated about its diameter produces a sphere.An isosceles triangle rotated about its axis of symmetry (the altitude from the vertex of the non-congruent angle) produces a cone.

（责任编辑：申月月）