Question

If the area of a circle is 58 square feet, find the circumference. A. 42.5 ft. B. 4.25 ft. C. 22.35 ft. D. 26.99 ft.

Answer 1

D. 26.99 ft

Explanation:

The formula for area of a circle is

A = πr², where r is the radius. We are given A = 58, so plug that in to find r...

58 = πr² solve for r...

58/π = r² (divide both sides by π)

√(58/π) = r (take the square root of both sides)

now simplify...

(√58)/(√π) = r

[(√58)(√π)]/[(√π)(√π)] = r

[√(58π)]/π = r

The formula for circumference is C = 2πr, where r is the radius....so we have

C = 2π([√(58π)]/π) now simplify...

C = 2√(58π) (the 2 pi's cancel out)

C = 26.9972124 (crunch in your calculator)

Answer 2

Answer: OPTION D.

Explanation:

The formula for calculate the circumference of a circle is:

`C=2r\pi`

Where r is the radius.

The formula for calculate the area of a circle is:

`A=r^2\pi`

Where r is the radius.

Solve for r from
`A=r^2\pi` to calculate it:

`r=\sqrt{(A)/(\pi)}\\r=\sqrt{(58ft^2)/(\pi)}\\r=4.296ft`

Subsitute the radius into
`C=2r\pi`. Then:

`C=(2)(4.296ft)\pi=26.99ft`