#118 – Math Tips

by Lisa Salzman

Back in the day, I was one of those students who liked math class. Call me crazy, but I liked the process and sequential steps of working out a problem. Today I have 5 kids and I find that some of them “get” math and others, not as much.

In the early days of NICET, they had Basic Math and Intermediate Math work elements. These two elements were required for various levels and subfield certifications. We’ve seen an increased interest in both of these topics in the past few weeks. We thought it would be a great way to get our brains working and a fun start to 2019.

Math can be fun! Let’s review a couple of basic exercises on Area and Volume.

Area is a two-dimensional measurement of the surface inside a plane (flat) geometric figure.

Volume is the amount of space occupied by a three-dimensional object, such as a box or tank.

Area and volume have different units of measurement that should never be mixed. Once you have picked a unit, you must convert all other units to the chosen unit. The following is a table which shows the two different types of units.    
Area, Volume Units Abbreviation
Area feet * feet = square feet sq. ft. or ft.2
Area inches * inches = square inches sq. in. or in.2
Volumefeet * feet * feet = cubic feet ft.3
Volume inches * inches * inches = cubic inches in.3

Area of a Rectangle:

Problem: Determine the area of a room having sides measuring 20 ft. and 15 ft.

Solution: The area (A) of a rectangle is length * width (L * W).

Our length (L) = 20 feet and our width (W) = 15 feet.

A = L * W Substitute length and width values

A = 20 ft. * 15 ft. Multiply

A = 300 ft.2

Note the units: Multiplying feet by feet = square feet (ft.2).

Remember, if this were a square room rather than a rectangular room, the formula for area would be the same (L * W).

Volume of a Rectangle

Suppose you need to find the volume of a rectangular tank, where the length is 200 ft., the width is 10 ft., and the depth is 12 ft.

Exercise #2: Find the volume of the tank shown below.

The volume (V) is determined by taking our cross-sectional area, which is the area of the bottom of the tank, and multiplying it by the depth (D) of the tank. In this case, the depth is 12 ft.

Solution #2: The formula for calculating volume is:

Volume = Area * Depth (or Volume = Length * Width * Depth)

V = L * W * D written in formula format

Our variables are:
  • Volume = V
  • Length = 200 ft.
  • Width = 10 ft.
  • Depth = 12 ft.

Substituting in the given values into the formula gives:

V = 200 ft. * 10 ft. * 12 ft.

V = 24,000 cubic feet or 24,000 ft.3

NOTE: Remember to watch your units and remember that feet * feet * feet equals cubic feet, or ft.3. Let us know if you would like to see more math samples in this blog.