# Area of a Circle

The formula for the area of a circle is:    A = pi × r2

If r is known, simply substitute the known value for r in the formula. Use 3.14 for pi.

Example #1:

Calculate A if r = 4 inches

A = pi × r2 = 3.14 × 42 = 3.14 ×16 = 50.24 inches2

Notice that the unit (inches) is squared to show that it was multiplied by itself twice

Example #2:

Calculate A if r = 6 inches

A = pi × r2 = 3.14 × 62 = 3.14 × 36 = 103.04 inches2

Examples #3

If D = 20 cm, calculate the area.

There is a couple of ways to solve this. The first way is to get r and then replace its value

Since r is half the diameter, r = 20 divided by 2

r = 10 cm

A = pi × r2 = 3.14 × 102 = 3.14 × 100 = 314 cm2

The other way to solve this is to use the diameter. We will need to express the formula in terms of the diameter.

The radius is half the diameter

r  =
d / 2

Replace r into the formula A = πr2.

Notice that r2 = r × r

 r × r =   d / 2 ×   d / 2
Notice that r2 = r × r

 r × r =   d / 2 ×   d / 2

r × r =
d × d / 2 × 2

r × r =
d2 / 4

A  =  π ×
d2 / 4

Let's us use the formula above now to see if we get the same answer.

A  =  3.14 ×
202 / 4

A  =  3.14 ×
400 / 4

A  =  3.14 × 100

A = 314 cm2

Examples #4

If A = 78.5 inches2, find r

Review solving multiplication equations before looking at the solution below.

r = 5 inches because 52 = 5 × 5 = 25

Related topics:

Approximate the area of a circle
Learn to approximate the area of a circle

Area of a sector
Learn to compute the area of a sector

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