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Using Formulas

Another important aspect of this unit is using formulas to determine measurements of items such as area and volume. Your booklet contains excellent pages showing the appropriate formulas for calculating area, surface area and volume of various shapes. This page will be dedicated on how to USE those formulas.

Example 1

Find the volume of a cone that has a radius of 15 cm and a height of 30 cm.

Solution

Looking at our formula sheet for volume, you can find that the formula for the volume of a cone is . This formula means that to find the volume of a cone (given by V) you have to calculate 1/3 TIMES PI TIMES THE RADIUS SQUARED TIMES THE HEIGHT. Let's substitute in the values that we know, namely the radius and the height. You get the following:

Following the order of operations we know we have to calculate the exponent first. That gives us:

Now, on your calculator, type the following:

(1 ÷ 3) x PI x 225 x 30

You should arrive at an answer of:

V = 7068.6

This means that the volume of the given cone is 7068.6 cm³. (Volume is always measured in units 'cubed').

Note the steps from the above example:

  1. Find the appropriate formula for the question.
  2. Substitute the values that you are given into the formula (replacing the variable in the formula).
  3. Calculate the answer using the order of operations.
  4. Write your final answer WITH APPROPRIATE UNITS.

These four steps are the same for any problem like this. Let's look at another example:

Example 2

Find the surface area of the rectangular solid shown below:

Solution

Step one is to find an appropriate formula. Looking at the surface area formulas in your booklet we find that the formula for the surface area of a rectangular solid is:

SA = 2lw + 2lh + 2wh

where l stands for length, w stands for width and h stands for height. Examining the diagram above we can see that l = 20", w = 10" and
h = 8". Placing these values into the formula (substituting) is step 2:

SA = 2(20)(10) + 2(20)(8) + 2(10)(8)

Now calculate the answer using the order of operations:

SA = 400 + 320 + 160
SA = 880

Now we must write our answer using appropriate units. The surface area of this rectangular solid is 880 in².

Now that you have looked at the examples, you can head back to the Design and Measurement main page.