8.4 Volume and Surface Area 489 Sphere Baseballs, tennis balls, and so on have the shape of a sphere (see the figure to the left). The formulas for the volume and surface area of a sphere are as follows. The derivation of the volume and surface area of a sphere are beyond the scope of this book. Cone Now consider the right circular cone illustrated in Fig. 8.37. When we use the term cone in this book, we mean a right circular cone. The volume of a cone is less than the volume of a cylinder that has the same base and the same height. In fact, the volume of the cone is one-third the volume of the cylinder. The formula for the surface area of a cone is the sum of the area of the circular base of the cone, r ,2 π and the area of the side of the cone, r r h , 2 2 π + or π π = + + SA r r r h . 2 2 2 The derivation of the area of the side of the cone is beyond the scope of this book. h r Figure 8.37 Volume and Surface Area of a Cone π π π = = + + V r h SA r r r h 1 3 2 2 2 2 r Volume and Surface Area of a Sphere π π = = V r SA r 4 4 3 3 2 Following is a summary of the formulas for the volumes and surface areas of the three-dimensional figures we have discussed thus far. Volumes and Surface Areas Rectangular Solid Cube Cylinder w h l s s s h r V lwh = V s3 = V r h2 π = SA lw wh lh 2 2 2 = + + SA s6 2 = SA rh r 2 2 2 π π = + Cone Sphere h r r π = V r h 1 3 2 π = V r 4 3 3 π π = + + SA r r r h 2 2 2 π = SA r 4 2
RkJQdWJsaXNoZXIy NjM5ODQ=