Intermediate Test Prep Math 8 (Grade 7) Calculating the Radius or Diameter of a Circle

Calculating the Radius or Diameter of a Circle - Lesson
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When given the circumference or area of a circle it is possible to calculate the radius or diameter of that circle.

Click here for definitions.

Formulas:

Circumference of a circle: C = πd

Area of a circle: A = πr²

Here is an example:

If the circumference of a circle is 50.27 in, find the diameter to the nearest whole number.

We'll substitute 50.27 in place of "C"
and solve for "d".

Calculator (remember to use the π button on your calculator instead of 3.14)

C = πd
50.27 = πd
(divide π from both sides to get "d" by itself)
50.27/π = d
d = 16 in

Here's another example:

If the circumference of a circle is 78.54 cm, find the radius to the nearest whole number.

We'll substitute 78.54 in place of "C"
and solve for "d".

C = πd
78.54 = πd
78.54/π = d
d = 25 cm

Now we must divide the diameter by 2 to find the radius : 12.5 cm

Now let's look at an example involving Area.

If the area of a circle is 201 m², find the radius to the nearest whole number.

We'll substitute 201 in place of "A"
and solve for "r".

A = πr²
201 = πr²
201/π = r²
64 = r²
(Now take the square root of both sides
to "un-do" the square.)
r = 8 m

(Numbers were rounded to the nearest whole number.)

Let's look at one more...

If the area of a circle is 12.57 sq in, find the diameter to the nearest whole number.

We'll substitute 12.57 in place of "A"
and solve for "r".

A = πr²
12.57 = πr²
12.57/π = r²
4 = r²
r = 2 in

Now we must double the radius for the diameter: 4 in

Now let's do some practice problems!

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