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QuestionFind the circumference of a circle with an area of 50.24 sq. yards, using π≈3.14\pi \approx 3.14.

Studdy Solution

STEP 1

Assumptions1. The area of the circle is50.24 square yards. We are using3.14 as the value for π\pi
3. The formula for the area of a circle is Area = \pi r^, where rr is the radius of the circle4. The formula for the circumference of a circle is Circumference=πrCircumference =\pi r, where rr is the radius of the circle

STEP 2

First, we need to find the radius of the circle. We can do this by rearranging the formula for the area of a circle to solve for rr.
r=Areaπr = \sqrt{\frac{Area}{\pi}}

STEP 3

Now, plug in the given values for the area and π\pi to calculate the radius.
r=50.243.14r = \sqrt{\frac{50.24}{3.14}}

STEP 4

Calculate the radius of the circle.
r=50.243.14≈4r = \sqrt{\frac{50.24}{3.14}} \approx4

STEP 5

Now that we have the radius, we can find the circumference of the circle using the formula for the circumference of a circle.
Circumference=2πrCircumference =2\pi r

STEP 6

Plug in the values for π\pi and the radius to calculate the circumference.
Circumference=2×3.14×4Circumference =2 \times3.14 \times4

STEP 7

Calculate the circumference of the circle.
Circumference=2×3.14×4=25.12Circumference =2 \times3.14 \times4 =25.12The circumference of the circle is approximately25.12 yards.

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