How do you find the Area of a circle that gives you its diameter?

For example.
The circles diameter is 30.2cm. The circles circumfrence is 94.828. How do you find the area of the circle?

You can use the fact that area of a circle is:

A = πr^2.

Note that we can use the circumference to find the radius as well. But we are already given the diameter! So who cares about doing that?

Since the diameter is twice the radius, we see that the radius is 30.2/2 = 15.1 cm. Plugging this into the formula for the area of a circle gives:

A = π(15.1)^2 = 228.01π ≈ 716.31 cm^2. <== ANSWER

I hope this helps!

This entry was posted on Wednesday, March 24th, 2010 at 5:33 pm and is filed under circle area. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

5 Responses to “How do you find the Area of a circle that gives you its diameter?”

Atlanta on March 24th, 2010 at 10:41 pm

times two.
References :
heckyes on March 24th, 2010 at 11:27 pm

the area of a circle is pi times the radius squared. the radius is half the diameter.
so (15.1 squared times pi) is your answer. a calculator will help with that
References :
Brian on March 25th, 2010 at 12:10 am

You can use the fact that area of a circle is:

A = πr^2.

Note that we can use the circumference to find the radius as well. But we are already given the diameter! So who cares about doing that?

Since the diameter is twice the radius, we see that the radius is 30.2/2 = 15.1 cm. Plugging this into the formula for the area of a circle gives:

A = π(15.1)^2 = 228.01π ≈ 716.31 cm^2. <== ANSWER

I hope this helps!
References :
Mark V on March 25th, 2010 at 12:18 am

Well, from what you’ve given me, you can find it two ways.

Knowing that area of a circle = pi * radius^2

(1) First, given the diameter

r = 0.5 * diameter
r = 0.5 * (30.2cm)
r = 15.1cm

Area = (3.14159) * (15.1 cm)^2
Area = (3.14159) * (228 cm^2)
Area = 716 cm^2

Or

(2) Given circumference is longer, but you can still get it

Equation for circumference of a circle = 2 * pi * r, find radius this way:

C = 2 * pi * r
94.828 cm = 2 * (3.14159) * r
94.828 cm = (6.28318) * r

r = 15.1 cm

From then on, it’s the same area equation, and you obviously get the same number.
References :
Geologist
antalg on March 25th, 2010 at 12:58 am

The formula for the area of a circle is:
r^2*pi
(radius squared multiplied by pi)

Since d=2r (the diameter is always equal to the radius multiplied by 2):
(d/2)^2*pi =
(30.2/2)^2*pi =
15.1^2 *pi =
228.01*pi =
716.315… cm^2
~ 716 cm^2
References :

Area List