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Calculating the Diameter and Circumference of a Circle
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1. Our Training Videos
Skills Application: Calculating the Diameter of a Circle
Step-by-Step: Calculating the Diameter of a Circle
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2. Running with Pi

## Tagged in

In 240 B.C. Eratosthenes, a Greek mathematician used geometry to calculate the circumference of the earth. He solved this problem by marking the position of the noontime sun at two different locations then he measured the angular difference between the two locations. This angular difference told him what fraction of the way around the earth separated the two locations. He then used this fraction to measure the distance between the two locations then calculated the distance around the whole earth.
“Diameter” is a Greek term that means “measure across” since the earth is 40,075.16 km in circumference the diameter of the earth then is 12,742 km

## Running with Pi

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3. Our Training Worksheets

FINDING THE DIAMETER

To find the diameter given the circumference divide the circumference by π.         D = C ÷ π

EXAMPLE:
What is the biggest diameter of the circle you can bend out of 18 in. of wire?

SOLUTION:

Diameter = 18 ÷ π = 18 ÷ 3.14 = 5.729 inches

FINDING THE CIRCUMFERENCE

To find the circumference of a circle, multiply the diameter with pi.        C = d ∙ π

This multiplication of course can be done the other way around as well:      C = π ∙ d

EXAMPLE:
Find the circumference of a hole with a diameter of 4.00 inches. Use π = 3.14

SOLUTION:
Circumference = d  × π = 4 × 3.14 = 12.56 in

Using the circumference formula to find the diameter of a circle

When the circumference is known, it is possible to find the diameter of a circle

Check out the ADVANCED section. The exercises will further your understanding and help with building a bigger mental picture. It builds links between numbers and algebra. It is important to try alternative calculations or approaches, to sketch the shapes, label the shapes with the given numbers, tracking changes to units of measure, visualizing to cross-link the concepts of perimeter and numbers. We use the numbers from this sheet metal pipe example. If you spend 20 – 40 min working with the different ideas in the ADVANCED page, youll remember key formulas easier and youll learn new skills faster.

### A Short Review

1.  To calculate the Circumference of a circle with a diameter of 5, you need to multiply the diameter by π:

C = d ∙ π
C = 5 x 3.14
C = 15.7

2.  To calculate the Diameter of a circle with a Circumference of 15, you need to divide the Circumference by π:

D = C ÷ π
D = 15 ÷ 3.14
D = 4.77

### Worksheet: Level 1

The operations used are clearly specified. Only one type of mathematical operation is used in a task.

### Worksheet: Level 1 Sample Question

Example:

1.  If you measured across a round water bottle lid, what part of the circle was measured?

1.  Diameter

### Worksheet: Level 2

Tasks involve one or two types of mathematical operation. Few steps of calculation are required.

### Worksheet: Level 2 Sample Question

Example:

Calculate the Diameter of the circle to 4 decimal places if the Circumference is:

C = 9 units

### Worksheet: Level 2 Sample Answer

C ÷ ? = d

Circumference ÷ ? = Diameter

9 ÷ ? = 2.8648 units

### Worksheet: Level 3

Tasks require a combination of operations. Several steps of calculation are required.

### Worksheet: Level 3 Sample Question

Examples:

1. How long is a round lid seal if its Diameter is 3 inches?

2. Whats the Diameter of a paper tube folded from a 279 mm long sheet?

### Worksheet: Level 3 Sample Answer

1.
C = d ∙ π
C = 3 x 3.14
C = 9.4248 inches

2.
D = C ÷ π
D = 279 ÷ 3.14
D = 88.8084 mm

Tasks involve multiple steps of calculation. Advanced mathematical techniques may be required.

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 ÷ p

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

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

You should see 10.82253613 on your display.

Calculate the circumference of a circle with a diameter of 10 inches.

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

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

Using a calculator, do the following:
Enter 10
Press x (multiplication) button (this could be omitted, depending on your calculators circuits)
Press p button or 2ndF button then the p button, depending on how your calculator is laid out.
Press =

>  You should see 31.41592654 on your display.

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

diameter x  p = circumference            circumference ÷ p = diameter

There is a third way to link C, d, and p into a formula:      circumference ÷ diameter = p

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

$\text{d x }{\pi}\text{ = C}$

$\frac{C}{\pi}\text{ = d}$

$\frac{C}{d}\text{ = }{\pi}$

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 dont do either one of these 2 things. Calculators are limited tools. They dont 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 p can combine in 3 ways:

If circumference is known, it can only be divided, either by diameter or p.

(C is always over d or
p, “over” implies fractions, and all fractions are divisions)

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

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

Some people like the 3 quantities arranged like fractions:

d x p = C
$\frac{C}{\pi}{= d}$

$\frac{C}{d}= \pi$

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

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

2 x 3 = 6
$\frac{6}{\color{Green}3}= {\color{Red} 2}$

$\frac{6}{\color{Red}2}= {\color{Green}{ 3}}$

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 p 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.