CHAPTER 12 Solid Geometry


cylinder is similar to a rectangular solid except that the base is a circle instead of a rectangle. To find the volume of a rectangular solid, we multiply the area of its rectangular base, w, by its height, h. For a cylinder, we do exactly the same thing. The volume of a cylinder is the area of its circular base, r2, times its height, h. The surface area of a cylinder depends on whether you are envisioning a tube, such as a straw without a top and bottom, or a can, which has both a top and bottom.

Key Fact K4

• The formula for the volume, V, of a cylinder whose circular base has radius r and whose height is h is V = r2h.

• The formula for the surface area, A, of the side of a cylinder is the product of the circumference of its circular base and its height: A = 2πrh.

• The areas of the top and bottom of a cylinder are each πr2, so the total surface area of a cylindrical can is 2πrh + 2πr2.

EXAMPLE 3: You can roll an 8 x 12 rectangular piece of paper into a cylinder in two ways. You could tape the 8-inch sides together, or you could tape the 12-inch sides together. Note that these cylinders do not have the same volume.

Cylinder I

Cylinder II

In cylinder I, C = 12  2πr = 12  r = , and so

In cylinder II, C =8  2π r = 8  r = , and so