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Verified Answer :

dexteright02

Data:
\(A_{cB} = 144 \pi ft^2\)
Circumference length = ?

Note¹: Knowing that the area of ​​the circle "B" is calculated by the following formula: \(A_{cB} = \pi *r^2\), using the data we have will find the value of the radius.

Data: \(A_{cB} = 144 \pi ft^2\)

Solving:
\(A_{cB} = \pi *r^2\)
\(144 \pi = \pi *r^2\)
\(\pi *r^2 = 144 \pi\)
\(r^2 = \frac{144 \diagup\!\!\!\!\!\pi }{ \diagup\!\!\!\!\!\pi }\)
\(r = \sqrt{144}\)
\(\boxed{r = 12\:ft}\)

Note²: Now, we will find the size of the circumference with the data already collected, so we will have:

Formula: \(C = 2* \pi *r\)
Adopting: \(\pi \approx 3.14\)

Solving:
\(C = 2* \pi *r\)
\(C = 2* 3.14 *12\)
\(\boxed{\boxed{C \approx 75.36\:ft}}\end{array}}\qquad\quad\checkmark\)

The area of circle B of radius 12 ft is 144 pi ft² then the circumference of circle B would be equal to 75.36 ft.

What is the circumference of the circle?

The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

The circumference of the circle = 2πr

The area of circle B is given as 144 pi ft². We need to find the circumference of the circle.

The area of the circle = \(\pi r^{2}\)

144 π ft² = \(\pi r^{2}\)

144 = r^2

r = √144

r = 12 ft

Now,

The circumference of the circle = 2πr

= 2 x π x r

= 2 x 3.14 x 12

= 75.36

Thus, the circumference of circle B is 75.36 ft.

Learn more about circumference here;

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