find the perimeter of the circle whose area = 25pi.
The answer to this question is that the circumference of the circle is 31.4 of whatever unit is being used. Here is how to find this answer.
The area of a circle is equal to pi times the radius squared. So that means that the radius of this circle is the square root of 25. That means that the radius is 5.
If the radius is 5, then the diameter is 10. The circumference of a circle is pi times the diameter. This means that the circumference is equal to
Therefore, circumference = 31.4
We know that the area of the circle is:
a = r^2 *pi = 25*pi
==> r^2 = 25
==> r = 5
Now we know that the circumference for the circle is:
C = 2r*pi
==> C = 2*5*pi = 10*pi
We know that pi= 22/7
==> C = 10*22/7 = 31.4 (approx.)
First, we have to establish that it is better to say the "circumference" of the circle, instead of the "perimeter" of the circle.
We know that the length of the circle, namely it's circumference, is:
L = 2*pi*r, where:
L - the length of the circle ( circumference)
pi - 3.14...
r - the radius of the circle
Wr don't know the area of the circle, yet.
We could calculate the radius of the circle, using the formula for the area of the circle:
A = pi*r^2
25pi = pi*r^2
We'll divide by pi both sides:
25 = r^2
sqrt 25 = sqrt r^2
r = 5
Now, we can calculate the circumference:
L = 2*pi*5
L = 10*pi
L = 10*3.14
The length is about 314 units.
To find the perimeter of the circle we need radius r. The perimeter of the circle is pi*r.
Given is the area 25pi. But area formula is pr^2. So pir^2 = 25. So r^2 = 25pi r = sqrt(25pi) = 5 sqrtpi.
So now Perimeter pi*r = pi*(5sqrtpi) = 5*pi*sqrtpi = 5*(pi)^(3/2) = 27.8416 units of length.