Certainly! Let's solve this step-by-step.
We are given that the area of a circle is [tex]\( 144\pi \)[/tex].
### Step 1: Recall the formula for the area of a circle
The area [tex]\( A \)[/tex] of a circle is given by the formula:
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
### Step 2: Solve for [tex]\( r \)[/tex] (the radius)
We know the area:
[tex]\[ A = 144\pi \][/tex]
Using the area formula:
[tex]\[ 144\pi = \pi r^2 \][/tex]
To find [tex]\( r \)[/tex], we first divide both sides of the equation by [tex]\( \pi \)[/tex]:
[tex]\[ 144 = r^2 \][/tex]
Next, we take the square root of both sides to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \sqrt{144} \][/tex]
[tex]\[ r = 12 \][/tex]
### Step 3: Recall the formula for the circumference of a circle
The circumference [tex]\( C \)[/tex] of a circle is given by the formula:
[tex]\[ C = 2\pi r \][/tex]
### Step 4: Substitute the radius into the circumference formula
Using the radius [tex]\( r = 12 \)[/tex]:
[tex]\[ C = 2\pi \times 12 \][/tex]
[tex]\[ C = 24\pi \][/tex]
### Step 5: Calculate the numerical value (if needed)
To express the circumference numerically:
[tex]\[ C \approx 24 \times 3.14159 \][/tex]
[tex]\[ C \approx 75.39822368615503 \][/tex]
Thus, the radius of the circle is [tex]\( 12 \)[/tex] and the circumference is approximately [tex]\( 75.40 \)[/tex].
