Intermediate Mathematics

Circumference of Circles

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Circumference of Circles

Circumference - The circumference is the distance around a circle.

Radius - The radius is a line segment from a point on a circle to its center.

Diameter - The diameter is a line segment joining two points on a circle and passing through its center.

Circumference of Circles

Regardless of where on the circle it is measured, the radius of any given circle is always the same length.

Also, the length of the radius of any circle is always one-half (\(\frac{1}{2}\)) the length of the diameter of that circle.

Circumference of Circles

The circumference of every circle is a little more than three times the length of its diameter.

This constant ratio of circumference to diameter is represented by the Greek letter π (pi) and is approximately equal to 3.14 or \(\frac{22}{7}\).

Circumference of Circles

You can check this relationship of circumference to diameter by putting a piece of string around circular objects of different sizes, such as cans, coins, and plates. Measure the string against a ruler, yard stick, or meter stick to find the circumference. Make a table like the one shown below, showing the diameter and circumference of each object you measure.

Circumference of Circles

Click on the correct answer.

What is the radius of the wheel?

Question 1 of 10

\(\color{#0a7d0a}{\frac{1}{2}}\) × 2 = 1
The radius of the wheel is 1 foot.

This is the approximate circumference of the circle. Multiply the diameter by \(\color{#be0a0a}{\frac{1}{2}}\) to find the radius. Try again.

This is the diameter of the circle. Multiply the diameter by \(\color{#be0a0a}{\frac{1}{2}}\) to find the radius. Try again.

You may have multiplied the diameter by 2. Multiply the diameter by \(\color{#be0a0a}{\frac{1}{2}}\) to find the radius. Try again.

One of these is the correct radius. Try again.

The length of the radius of any circle is always \(\color{#be0a0a}{\frac{1}{2}}\) the length of the diameter of that circle.

Circumference of Circles

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What is the approximate circumference of the coin?

Question 2 of 10

3 × 8 = 24
The approximate circumference of the coin is 24 cm.

This is the radius. The circumference of every circle is a little more than 3 times the length of its diameter. Try again.

You may have multiplied the diameter by the radius. The circumference of every circle is a little more than 3 times the length of its diameter. Try again.

You may have multiplied the diameter by 2. The circumference of every circle is a little more than 3 times the length of its diameter. Try again.

One of these is the approximate circumference. Try again.

The circumference of every circle is a little more than 3 times the length of its diameter.

Circumference of Circles

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About how many times longer is the circumference than the diameter of this circle?

2 times

The circumference and the diameter are the same

3 times

4 times

None of these

Question 3 of 10

The circumference is more than 2 times the diameter of the circle. Try again.

The diameter is always smaller than the circumference. Try again.

The circumference is about 3 times the diameter of the circle.

The circumference is less than 4 times the diameter of the circle. Try again.

One of these is the correct answer. Try again.

The circumference of this circle is approximately 27 meters.

Circumference of Circles

The ratio of circumference to diameter (C ÷ d) is always π. This means that the circumference (C) is always about 3.14 (π) times the diameter (d).

The formula below allows you to easily calculate the circumference of a circle when you know its diameter.

Circumference of Circles

To find the circumference of a circle, multiply π times the diameter of the circle. Use 3.14 for π.

In the example above, the diameter of the circle is 6.2 ft.

C = π · d
C = 3.14 × 6.2
C = 19.468

The circumference of the circle is 19.468 feet.

Circumference of Circles

Click on the circumference.

A major league baseball bat may not be more than 7 cm in diameter at its thickest point. What is the largest possible circumference of a major league bat?

Question 4 of 10

You may have multiplied the diameter by the radius. To find the circumference, multiply π times the diameter (C= π · d). Try again.

This is the largest possible radius of the bat. To find the circumference, multiply π times the diameter (C = π · d). Try again.

You may have used the value 31.4 for π. Remember that π is equal to 3.14. Try again.

You may have multiplied the diameter by 2. To find the circumference, multiply π times the diameter (C = π · d). Try again.

3.14 × 7 = 21.98
The largest possible circumference of the bat is 21.98 cm.

This is the correct formula:
C = π·d

Circumference of Circles

Click on the circumference.

Question 5 of 10

You may have used the value 31.4 for π. Remember that π is equal to 3.14. Try again.

You may have used the value 314 for π. Remember that π is equal to 3.14. Try again.

You may have used the value 0.314 for π. Remember that π is equal to 3.14. Try again.

3.14 × 3.5 = 10.99
The circumference is 10.99 yd.

One of these is the correct circumference. Try again.

This is the correct formula:
C = π · d

Circumference of Circles

Click on the circumference.

This orange has a diameter of 3 inches. What is the circumference?

Question 6 of 10

You may have used the value 31.4 for π. Remember that π is equal to 3.14. Try again.

3.14 × 3 = 9.42
The circumference of the orange is 9.42 inches.

You may have multiplied the diameter by 2. To find the circumference, multiply π times the diameter (C = π · d). Try again.

You may have multiplied the diameter by the radius. To find the circumference, multiply π times the diameter (C = π · d). Try again.

One of these is the correct circumference. Try again.

This is the correct formula:
C = π · d

Circumference of Circles

The radius of any circle is equal to one-half (\(\frac{1}{2}\)) the diameter. In other words, 2·r is the same as the diameter.

If you are given the radius of a circle instead of its diameter, it is easy to calculate the circumference (C). Multiply the radius (r) by 2, and then multiply by π.

The formula below allows you to easily calculate the circumference of a circle when you know its radius.

Circumference of Circles

To find the circumference of a circle, multiply the radius by 2, and then multiply by π. Use 3.14 for π.

In the example above, the radius of the circle is 3.5 meters.

C = 2 · π · r
C = 2 × 3.14 × 3.5
C = 3.14 × 7
C = 21.98

The circumference of the circle is 21.98 meters.

Circumference of Circles

Click on the circumference.

The metal ring that holds a basketball net has a radius of 23 cm. What is the circumference of the metal ring?

Question 7 of 10

You may have used the value 2.14 for π. Remember that π is equal to 3.14. Try again.

C = 2 × 3.14 × 23
The circumference of the metal ring is 144.44 cm.

You may have multiplied the radius by π, but did not multiply by 2. To find the circumference, multiply 2 times π times the radius (C = 2 · π · r). Try again.

The diameter is 46 cm. Multiply this diameter by 3.14 to find the circumference. Try again.

One of these is the correct circumference. Try again.

This is the correct formula:
C = 2 · π · r

Circumference of Circles

Click on the circumference.

What is the circumference of a circle with a radius of 3 inches?

Question 8 of 10

You may have used the value 3.114 for π. Remember that π is equal to 3.14. Try again.

The diameter is 6 inches. Multiply this diameter by 3.14 to find the circumference. Try again.

You may have multiplied π by the radius, but you did not multiply by 2. To find the circumference, multiply 2 times π times the radius (C = 2 · π · r). Try again.

C = 2 × 3.14 × 3
The circumference of the circle is 18.84 inches.

One of these is the correct circumference. Try again.

This is the correct formula:
C = 2·π·r

Circumference of Circles

Click on the circumference.

A group of your friends and you clean swimming pools for extra money. Your job is to clean around the edge of a circular pool that has a radius of 7.5 ft. How many feet will you need to clean?

Question 9 of 10

You may have multiplied the radius by 2, but then added π. To find the circumference, multiply 2 times π times the radius (C = 2 · π · r). Try again.

You may have multiplied the radius by π, but did not multiply by 2. To find the circumference, multiply 2 times π times the radius (C = 2 · π · r). Try again.

The diameter is 15 feet. Multiply this diameter by 3.14 to find the circumference. Try again.

C = 2 × 3.14 × 7.5
You need to clean 47.1 feet around the edge of the pool.

One of these is the correct circumference. Try again.

This is the correct formula:
C = 2 · π · r

Circumference of Circles

Click on the circumference.

Question 10 of 10

You may have multiplied the radius by π, but did not multiply by 2. To find the circumference, multiply 2 times π times the radius (C = 2 · π · r). Try again.

You may have the value 3.114 for π. Remember that π is equal to 3.14. Try again.

C = 2 × 3.14 × 12
The circumference of the circle is 75.36 meters.

The diameter is 24 meters. Multiply this diameter by 3.14 to find the circumference. Try again.

One of these is the correct circumference. Try again.

This is the correct formula:
C = 2 · π · r

Multiplication of Decimals