Math: Solving Formula Problems

Formula on the GED test are most commonly used to solve the area and volume of shapes and figures.  During the test, you will have the ability to click on a link that brings up a sheet of formulas, so do not worry about needing to memorize these (although doing so would save time).  However, you do need to practice plugging numbers into a formula in order to solve.

Whenever you see two letters or a number and a letter right next to each other (i.e., 4x,  lw, 2B), that means you multiply the two together.  For example:

The formula for the area of a rectangle is A = lw, which means: 

Area = length x width.

So, given a problem where the length of a rectangle is 20 and the width is 9, the area is calculated as:

A = lw       A = 20 x 9    A = 180

Let's look at the formula to calculate the surface area of a cylinder:

SA = 2πrh + 2πr²

This looks complicated, but let's take it one step at a time.  Let's say we have the following problem:

A cylinder has a height of 10 meters.  Its base has a radius of 3 meters.  What is its surface area?

Believe it or not, those two numbers are actually enough to solve the problem.  In the formula above, r = radius, and h = height.  π is pi, a number that is approximately 3.14; however, there is a π on your calculator that you can use!  The only other issue is the exponent at the end of the problem, but let's first plug in the numbers:

SA = 2πrh + 2πr²

SA =     2  x  π  x  3  x  10     +    2  x  π  x  3²

If we go by order of operations, EXPONENTS come first, so solve 3², which is 3 to the second power, or 3 x 3, which is 9.  Then plug 9 in where 3² was:

SA =     2  x  π  x  3  x  10     +    2  x  π  x  9

Now, we solve the MULTIPLICATION next.  Use your calculator to multiply everything BEFORE the addition sign and plug that answer in.  Use your calculator to multiply everything AFTER the addition sign and plug that number in.  It's okay to round to a couple decimal places.  Your problem would look like this:

SA =   188.50  +  56.55

Now, just add the two numbers together to get the answer:  245.05 m²

**Note that area problems will always end in units squared.

Let's practice some problems using formulas.  First, here's the link to the official formula sheet that will appear on the GED test.  Click on it and keep it up as you do the rest of the problems:

GED 2014 Formula Sheet

Here is a link that describes two-dimensional and three-dimensional geometric shapes and figures:

List of Geometric Shapes

Here's a link to solving some area problems.  Two things to remember: 1) the radius of a circle is HALF the diameter.  2)  A semicircle is a half circle, so to calculate the radius or circumference, calculate the WHOLE circle, and divide your answer by two.

Area Practice

Here's three links to solving various volume problems (you may need information from the geometric shape link above to solve some of the problems):

Prisms Practice

Pyramids Practice

Cylinders, Cones, and Spheres Practice