The surface area of a three-dimensional solid is the sum of the areas of the faces of the solid. Surface area is a different concept from that of volume. For example, surface area is the amount of sheet metal needed to build a rectangular fuel tank while volume is the amount of fuel that the tank can contain.

**Rectangular Solid**

The formula for the surface area of a rectangular solid [Figure 1-24] is given as:

Surface Area =

2 × [(Width × Length) + (Width × Height) + (Length × Height)] = 2 × [(W × L) + (W × H) + (L × H)]**Cube**

The formula for the surface area of a cube [Figure 1‑25] is given as:

Surface Area = 6 × (Side × Side) = 6 × S^{2}

Example: What is the surface area of a cube with a side measure of 8 inches?

Surface Area = 6 × (Side × Side)

= 6 × S^{2}= 6 × 8

^{2}= 6 × 64 = 384 square inches

**Cylinder**

The formula for the surface area of a cylinder [Figure 1-26] is given as:

Surface Area = 2 × π × radius^{2}+ π × diameter × height = 2 × π × r

^{2}+ π × D × H

**Sphere**

The formula for the surface area of a sphere [Figure 1-28] is given as:

Surface Area = 4 × π × radius^{2}= 4 × π × r

^{2}

**Cone**

The formula for the surface area of a right circular cone [Figure 1-29] is given as:

Surface Area = π × radius × [radius + (radius^{2 }+ height

^{2})

^{1⁄2}] = π × r × [r + (r

^{2}+ H

^{2})

^{1⁄2}]

Figure 1-30 summarizes the formulas for computing the volume and surface area of three-dimensional solids.