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

Surface Area = 6 x (Side x Side) = 6 x S2

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

Surface Area = 6 × (Side × Side)
                  = 6 × S2 = 6 × 82 = 6 × 64
                  = 384 square inches


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


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


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

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

Trigonometric Functions

Trigonometry is the study of the relationship between the angles and sides of a triangle. The word trigonometry comes from the Greek trigonon, which means three angles, and metro, which means measure.

Right Triangle, Sides and Angles

In Figure 1-31, notice that each angle is labeled with a capital letter. Across from each angle is a corresponding side, each labeled with a lower case letter. This triangle is a right triangle because angle C is a 90° angle. Side a is opposite from angle A, and is sometimes referred to as the “opposite side." Side b is next to, or adjacent to, angle A and is therefore referred to as the “adjacent side." Side c is always across from the right angle and is referred to as the “hypotenuse."

Sine, Cosine, and Tangent

The three primary trigonometric functions and their abbreviations are: sine (sin), cosine (cos), and tangent (tan). These three functions can be found on most scientific calculators. The three trigonometric functions are actually ratios comparing two of the sides of the triangle as follows:

Example: Find the sine of a 30° angle.

Calculator Method:

Using a calculator, select the “sin" feature, enter the number 30, and press “enter." The calculator should display the answer as 0.5. This means that when angle

A equals 30°, then the ratio of the opposite side (a) to the hypotenuse (c) equals 0.5 to 1, so the hypotenuse is twice as long as the opposite side for a 30° angle. Therefore, sin 30° = 0.5.

Trigonometric Table Method:

When using a trigonometry table, find 30° in the first column. Next, find the value for sin 30° under the second column marked “sine” or “sin.” The value for sin 30° should be 0.5.


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