Mathematics in Aviation Maintenance

A solid with a circle as a base and with sides that gradually taper to a point is called a cone. [Figure 3-29] The formula for the volume of a cone is given as:

Formula: v = 1/3 × π × radius2 × height = 1/3 × π × r2 × h

Since all volumes are not measured in the same units, it is necessary to know all the common units of volume and how they are related to each other. For example, the mechanic may know the volume of a tank in cubic feet or cubic inches, but when the tank is full of gasoline, they are interested in how many gallons it contains. Refer to Figure 3-23, Applied Mathematics Formula Sheet, for a comparison of different units of volume.

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.

The formula for the surface area of a rectangular solid [Figure 3-24] is given as:

Formula: Surface area = ; 2 × [(width × length) + (width × height) + (length × height)] ; = 2 × [(w × l) + (w × h) + (l × h)]

The formula for the surface area of a cube [Figure 3-25] is given as:

Formula: Surface area = 6 × (side × side) = 6 × s2

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

Formula: Surface area = 6 × (side × side) ; = 6 × S2 = 6 × 82 = 6 × 64 ; = 384 square inches

The formula for the surface area of a cylinder [Figure 3-26] is given as:

Formula: Surface area = 2 × π × radius2 + π × diameter × height ; = 2 × π × r2 + π × d × h

Aviation Training Experts™

Aviation Maintenance Technician Handbook–General

Cone

Units of Volume

Computing Surface Area of Three-Dimensional Solids

Rectangular Solid

Cube

Cylinder