The area of a circle is 16pi ft^2 .What is the circumference, in feet? Express your answer in terms of pi Answer

To find the circumference of the circle, we first need to determine its radius. The formula for the area of a circle is given by:<br /><br />\[<br />A = \pi r^2<br />\]<br /><br />where \( A \) is the area and \( r \) is the radius. We know that the area is \( 16\pi \), so we can set up the equation:<br /><br />\[<br />\pi r^2 = 16\pi<br />\]<br /><br />Dividing both sides by \(\pi\), we get:<br /><br />\[<br />r^2 = 16<br />\]<br /><br />Taking the square root of both sides, we find:<br /><br />\[<br />r = 4<br />\]<br /><br />Now that we have the radius, we can find the circumference using the formula:<br /><br />\[<br />C = 2\pi r<br />\]<br /><br />Substituting \( r = 4 \) into the formula gives:<br /><br />\[<br />C = 2\pi \times 4 = 8\pi<br />\]<br /><br />Therefore, the circumference of the circle is \( 8\pi \) feet.