Technical Mathematics, Sixth Edition

6.6. Cylinder, Cone, and Sphere

Let us turn now from the polyhedra, solids bounded by planes, to solids bounded by curved surfaces. They are the cylinder, cone, and sphere.

6.6.1. The Cylinder

A cylinder is a solid with two parallel, identical faces (called bases), whose lateral surface is formed by joining corresponding points on the bases (Fig. 6-106). A cylinder is named according to the shape of its bases (i.e., circular cylinder, elliptical cylinder, and so forth). The axis of a cylinder is the line connecting the centers of its bases. A cylinder is called right if its bases are perpendicular to its axis; otherwise it is called oblique. The altitude of a cylinder is the perpendicular distance between the bases.

Figure 6.106. Right circular cylinder.

Example 28: Find (a) the volume and (b) the lateral area of a right circular cylinder having a base radius of 5.73 units and an altitude of 8.24 units. Solution: (a) The area of the circular base is A = π(5.73)2 = 103 square units So the volume of the cylinder is (b) The perimeter of the base is P = 2π(5.73) = 36.0 units so the lateral area is then

Example 29: An Application. A cylindrical form for a right circular concrete ...