12/26/2016
(67) Radius, diameter, & circumference | Area and circumference of circles | Area and perimeter | Geometry | Khan Academy
Radius, diameter, & circumference
Learn the relationship between the radius, diameter, and circumference of a circle.
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What is a circle?
We've all seen circles before. They have this perfectly round shape, which makes
them perfect for hoola-hooping!
Every circle has a center, which is a point that lies exactly at the... well... center of the
circle. A circle is a shape where distance from the center to the edge of the circle is
always the same:
Center
You might have suspected this before, but in fact, the distance from the center of a
circle to any point on the circle itself is exactly the same.
Radius of a circle
This distance is called the radius of the circle.
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12/26/2016
(67) Radius, diameter, & circumference | Area and circumference of circles | Area and perimeter | Geometry | Khan Academy
Radius
Which of the segments in the circle below is a radius?
Select all that apply.
A
B
C
B
A
C
Check
Diameter of a circle
The diameter is the length of the line through the center that touches two points on
the edge of the circle.
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(67) Radius, diameter, & circumference | Area and circumference of circles | Area and perimeter | Geometry | Khan Academy
Diameter
Which of the segments in the circle below is a diameter?
Select all that apply.
A
B
A
C
B
C
Check
Notice that a diameter is really just made up of two radii (by the way, "radii" is just
the plural form of radius):
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(67) Radius, diameter, & circumference | Area and circumference of circles | Area and perimeter | Geometry | Khan Academy
Diameter
Radius
Radius
So, the diameter d of a circle is twice the radius r :
d = 2r
Find the diameter of the circle shown below.
units
6
Check
[Show answer]
Find the radius of the circle shown below.
units
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(67) Radius, diameter, & circumference | Area and circumference of circles | Area and perimeter | Geometry | Khan Academy
10
Check
[Show answer]
Circumference of a circle
The circumference is the distance around a circle (its perimeter!):
Circumference
Here are two circles with their circumference and diameter labeled:
Circle 2:
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(67) Radius, diameter, & circumference | Area and circumference of circles | Area and perimeter | Geometry | Khan Academy
Circle 2:
Circumference ≈ 6.28318...
Circle 1:
Circumference ≈ 3.14159...
Diameter = 1
Diameter = 2
Let's look at the ratio of the circumference to diameter of each circle:
Circumference
:
Diameter
Circle 1
Circle 2
3.14159...
= 3.14159...
1
6.28318...
= 3.14159...
2
Fascinating! The ratio of the circumference C to diameter d of both circles
is 3.14159...
C
= 3.14159...
d
This turns out to be true for all circles, which makes the number 3.14159... one of
the most important numbers in all of math! We call the number pi (pronounced like
the dessert!) and give it its own symbol π .
C
=π
d
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(67) Radius, diameter, & circumference | Area and circumference of circles | Area and perimeter | Geometry | Khan Academy
Multiplying both sides of the formula by d gives us
C = πd
which let's us find the circumference C of any circle as long as we know the
diameter d.
Using the formula C
= πd
Let's find the circumference of the following circle:
10
The diameter is 10, so we can plug d
= 10 into the formula C = πd:
C = πd
C = π ⋅ 10
C = 10π
That's it! We can just leave our answer like that in terms of π . So, the circumference
of the circle is 10π units.
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(67) Radius, diameter, & circumference | Area and circumference of circles | Area and perimeter | Geometry | Khan Academy
Your turn to give it a try!
Find the circumference of the circle shown below.
Enter an exact answer in terms of π .
units
6
Check
[I need help! Please show me the solution.]
Challenge problem
?
5
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Find the arc length of the semicircle.
Enter an exact answer in terms of π .
units
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