What is circumference?

This question is not easy to answer and even more complicated to understand. If you imagine any point on a flat surface and a series of points whose distance from that point is identical, then you are looking at a circle.

B - What is circumference

Practice Circle

examples with solutions for circle

Exercise #1

Given the circle whose diameter is 7 cm

What is your area?

777

Video Solution

Step-by-Step Solution

First, let's remember the formula for the area of a circle:

 πr2 \pi r^2

In the question, we are given the diameter of the circle, but we need the radius.

It is known that the radius is actually half of the diameter, therefore:

r=7:2=3.5 r=7:2=3.5

We replace in the formula

π3.52=12.25π \pi3.5^2=12.25\pi

Answer

12.25π 12.25\pi cm².

Exercise #2

Look at the circle in the figure.

What is its circumference if its radius is equal to 6?

6

Video Solution

Step-by-Step Solution

Formula of the circumference:

P=2πr P=2\pi r

We replace the data in the formula:

P=2×6×π P=2\times6\times\pi

P=12π P=12\pi

Answer

12π 12\pi

Exercise #3

O is the center of the circle in the diagram below.

What is its area?

333OOO

Video Solution

Step-by-Step Solution

Remember that the formula for the area of a circle is

πR²

 

We replace the data we know:

π3²

π9

 

Answer

9π 9\pi cm²

Exercise #4

Look at the circle in the figure:

777

The radius is equal to 7.

What is the area of the circle?

Video Solution

Step-by-Step Solution

Remember that the formula for the area of a circle is

πR²

 

We replace the data we know:

π7²

π49

Answer

49π

Exercise #5

Look at the circle in the figure:

444

Its radius is equal to 4.

What is its circumference?

Video Solution

Step-by-Step Solution

The formula for the circumference is equal to:

2πr 2\pi r

Answer

examples with solutions for circle

Exercise #1

A circle has a circumference of 31.41.

What is its radius?

Video Solution

Step-by-Step Solution

To solve the exercise, first we must remember the circumference formula:

P=2πR P= 2\pi R

P is the circumference and Pi has a value of 3.14 (approximately).

We substitute in the known data:

31.41=23.141R 31.41=2\cdot3.141\cdot R

Keep in mind that the result can be easily simplified using Pi:

31.413.141=2R \frac{31.41}{3.141}=2R

10=2R 10=2R

Finally, we simplify by 2:

5=R 5=R

Answer

5

Exercise #2

A circle has a circumference of 50.25.

What is its radius?

Video Solution

Step-by-Step Solution

We use the formula:

P=2πr P=2\pi r

We replace the data in the formula:

50.25=3.14×2r 50.25=3.14\times2r

50.25=2×r×3.14 50.25=2\times r\times3.14

50.25=6.28r 50.25=6.28r

50.256.28=6.28r6.28 \frac{50.25}{6.28}=\frac{6.28r}{6.28}

r=8 r=8

Answer

8

Exercise #3

O is the center of the circle in the figure below.

888OOO What is its circumference?

Video Solution

Step-by-Step Solution

We use the formula:P=2πr P=2\pi r

We replace the data in the formula:P=2×8π P=2\times8\pi

P=16π P=16\pi

Answer

16π 16\pi cm

Exercise #4

A circle has an area of 25 cm².

What is its radius?

Video Solution

Step-by-Step Solution

Area of the circle:

S=πr2 S=\pi r^2

We replace the data we know:

25=πr2 25=\pi r^2

Divide by Pi:25π=r2 \frac{25}{\pi}=r^2

Extract the root:25π=r \sqrt{\frac{25}{\pi}}=r

5π=r \frac{5}{\sqrt{\pi}}=r

Answer

5π \frac{5}{\sqrt{\pi}} cm

Exercise #5

Look at the circle in the figure:

131313

The diameter of the circle is 13.

What is its area?

Video Solution

Step-by-Step Solution

First, let's remember what the formula for the area of a circle is:

S=πr2 S=\pi r^2

The problem gives us the diameter, and we know that the radius is half of the diameter therefore:

132=6.5 \frac{13}{2}=6.5

We replace in the formula and solve:

S=π×6.52 S=\pi\times6.5^2

S=42.25π S=42.25\pi

Answer

42.25π

examples with solutions for circle

Exercise #1

Look at the circle in the diagram.

AB is a chord.

Is it possible to calculate the area of the circle?

555AAABBB

Video Solution

Step-by-Step Solution

Since AB is just a chord and we know nothing else about the diameter or the radius, we cannot calculate the area of the circle.

Answer

It is not possible.

Exercise #2

Given the semicircle:
141414
What is the area?

Video Solution

Step-by-Step Solution

Formula for the area of a circle:

S=πr2 S=\pi r^2

We complete the shape into a full circle and notice that 14 is the diameter.

A diameter is equal to 2 radii, so:r=7 r=7

We replace in the formula:S=π×72 S=\pi\times7^2

S=49π S=49\pi

Answer

24.5π

Exercise #3

A circle has a circumference of 31.41.

What is its radius?

Video Solution

Step-by-Step Solution

To solve the exercise, first we must remember the circumference formula:

P=2πR P= 2\pi R

P is the circumference and Pi has a value of 3.14 (approximately).

We substitute in the known data:

31.41=23.141R 31.41=2\cdot3.141\cdot R

Keep in mind that the result can be easily simplified using Pi:

31.413.141=2R \frac{31.41}{3.141}=2R

10=2R 10=2R

Finally, we simplify by 2:

5=R 5=R

Answer

5

Exercise #4

The circumference of a circle is 14.

How long is the circle's radius?

Video Solution

Step-by-Step Solution

We use in the formula:

P=2πr P=2\pi r

We replace the data in the formula:

14=2×π×r 14=2\times\pi\times r

We divide Pi by 2:

142π=2πr2π \frac{14}{2\pi}=\frac{2\pi r}{2\pi}

7π=r \frac{7}{\pi}=r

Answer

7π \frac{7}{\pi}

Exercise #5

A circle has a circumference of 50.25.

What is its radius?

Video Solution

Step-by-Step Solution

We use the formula:

P=2πr P=2\pi r

We replace the data in the formula:

50.25=3.14×2r 50.25=3.14\times2r

50.25=2×r×3.14 50.25=2\times r\times3.14

50.25=6.28r 50.25=6.28r

50.256.28=6.28r6.28 \frac{50.25}{6.28}=\frac{6.28r}{6.28}

r=8 r=8

Answer

8