Question

NOTE: THIS IS A TUTORIAL. NOT A QUESTION.





How to use formulas.

Answer 1

I'm making this tutorial on how to use formulas because I have noticed that there are a number of times in which someone asks a question that can easily be solved by using a formula. Many of us simply give the formula expecting them to be able to solve it and ask us if they got the answer correct. However, what happens is they ask how do I use the formula? Well here is an explanation on how formulas work.

A formula is basically a set of instructions to get a certain result. There are all types of formulas such as formulas to find area, surface area, volume, etc. A formula is made up of numbers, letters, and symbols. Symbols usually represent a definite value. The letters usually represent values that change based on the problem. In order to use a formula, you have to "plug in" values for the letters and symbols they represent. Let's take a look at an example.
EXAMPLE:
Find the area of a circle with radius 9. Leave in terms of π.
The formula for the area of a circle is:
\[A = πr^{2}\]
where r = radius
Now, the problem has given you the radius which is necessary to find the area. The radius is 9. Now, when you "plug in" the values, substitute the values in for their respective letters/symbols.
\[A = πr^{2}\]
\[A = π(9)^{2}\]
\[A = 81π\]
There you go! It says leave it in terms for π, so this is the answer.
Now, if the problem were:
Find the area of a circle with radius 9. Use 3.14 for π.
You'd plug in that value for the symbol π.
\[A = 81π\]
\[A = 81(3.14)\]
\[A ≈ 254.34\]
There you have it! You'll notice that the sign ≈ has replaced the = sign. The ≈ sign means approximately. 3.14 is an approximate value for π. The values of π is endless.
π ≈ 3.14159265...
Now, there are times in which you will be given a value, and have to use this value to figure out other values. Let's take another look at the formula for the area of a circle.
EXAMPLE:
Find the area of a circle that has a circumference of 30π. Leave it in terms of π.
The formula for the circumference of a circle is:
\[C = 2πr\]
The formula for the area of a circle is once again:
\[A = πr^{2}\]
Now, you have to once again plug in values. Since you don't have anything to find the area, you have to use the formula for circumference first.
\[C = 2πr\]
\[30π = 2πr\]
Look what happened! The formula became an equation in which you have to solve for a value! Now you just have to solve for the radius algebraically.
\[15 = r\]
Now just plug the new value into the formula for the area of a circle.
\[A = πr^{2}\]
\[A = π(15)^{2}\]
\[A = 225π\]
There we go. That is the end to this little tutorial. Using formulas are critical to math and will never go away. It's really quite simple once you reason it out! Now all you have to do is take the effort to memorize the formulas now that you know how to use formulas!