Calculating the Diameter and Circumference of a Circle - GetMath

[Pages:3]Calculating the Diameter and Circumference of a Circle

Another Way to Get the Answer

Task: Calculate the diameter of a pipe made from a rectangular sheet of metal with a length of 34 inches.

One way to get the answer, using the formula d = C ?

Layout your calculations neatly, so you can review, track changes, correct or learn from them. One way a layout can look like is this:

1 d = C ?

c = 34 in

d = ? in

2

c = 34 in

d = C ?

d = ? in

diameter = circumference ?

4

c = 34 in

d = C ?

d = ? in

diameter = circumference ?

d

= 34 ?

3

c = 34 in

d = C ?

d = ? in

diameter = circumference ?

d

= 34 ?

d

= 10.8 in

Using a calculator, do the following: Enter 34 Press ? button Press ? button or 2ndF button then the button, depending on how your calculator is laid out. Press =

You should see 10.82253613 on your display.

Calculating the Diameter and Circumference of a Circle

Another Way to Get the Answer

Task: Calculate the circumference of a circle with a diameter of 10 inches. One way to get the answer, using the formula C = d ? Layout your calculations neatly, so you can review, track changes, correct or learn from them. One way a layout can look like is this:

1 C = d ?

c = ? in

d = 10 in

2

c = ? in

C = d ?

d = 10 in

circumference = diameter ?

3

c = ? in

C = d ?

d = 10 in

circumference = diameter ?

C = 10 x 3.1416

4

c = ? in

C = d ?

d = 10 in

circumference = diameter ?

C = 10 x 3.1416

C = 31.4159 in

Using a calculator, do the following: Enter 10 Press x (multiplication) button (this could be omitted, depending on your calculator`s circuits)

Press button or 2ndF button then the button, depending on how your calculator is laid out. Press =

You should see 31.41592654 on your display.

ADVANCED

Look at the circumference formulas in the above 2 tasks. The calculations use 2 different formulas. However, both formulas have C, d, and

diameter x = circumference

circumference ? = diameter

There is a third way to link C, d, and into a formula:

circumference ? diameter =

Words of the above 3 formulas can be replaced with only letters. This is how they look like:

Calculating the Diameter and Circumference of a Circle

d x = c

= c

=

To solve circle problems efficiently, you need to be able to:

1. identify which calculation to do (based on word clues) and

2. you have to remember the formula to use accordingly.

Contrary to popular belief, calculators are not much help as they don`t do either one of these 2 things. Calculators are limited tools. They don`t do the thinking or the math. They only calculate.

The following visual of a triangle may help to help you get started with memorizing the circle formulas and their relationships:

Circumference, diameter and can combine in 3 ways: If circumference is known, it can only be divided, either by diameter or

C (c is always over d or "over" implies fractions, and all fractions are divisions)

If diameter and are given, they are to be multiplied.

d

(In formulas, amounts for multiplication are always written side-by-side)

Some people like the 3 quantities arranged like fractions:

d x = c

= c

=

These letters can be replaced by numbers to see an interesting relationship.

C can be replaced by 6, d can be 2 and is just 3 for now.

2 x 3 = 6

6

= 2

6

= 3

Notice that in fractions the 3 and the 2 (the denominator and the result) can trade places. This fraction fact may help memorize the formulas knowing that if circumference (c) is given a division must follow. Likewise, if only diameter is given, a multiplication by must follow.

A formula is a symbolic short-hand way to write calculation procedures. Use a memory jogger that`s easiest to remember for you.

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