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QuestionFind the area of a circular rug with a circumference of 10.048 yards. Use π≈3.14\pi \approx 3.14 and round to the nearest hundredth.

Studdy Solution

STEP 1

Assumptions1. The rug is circular. The circumference of the rug is10.048 yards3. We are using3.14 as the value for π\pi
4. The area of a circle is given by the formula Area = \pi r^, where rr is the radius of the circle5. The circumference of a circle is given by the formula Circumference=πrCircumference =\pi r, where rr is the radius of the circle

STEP 2

First, we need to find the radius of the rug. We can do this by rearranging the formula for the circumference of a circle to solve for rr.
r=Circumference2πr = \frac{Circumference}{2\pi}

STEP 3

Now, plug in the given values for the circumference and π\pi to calculate the radius.
r=10.0482×3.14r = \frac{10.048}{2 \times3.14}

STEP 4

Calculate the radius.
r=10.0486.28=1.6 yardsr = \frac{10.048}{6.28} =1.6\, yards

STEP 5

Now that we have the radius, we can find the area of the rug using the formula for the area of a circle.
Area=πr2Area = \pi r^2

STEP 6

Plug in the values for π\pi and the radius to calculate the area.
Area=3.14×(1.6)2Area =3.14 \times (1.6)^2

STEP 7

Calculate the area of the rug.
Area=3.14×2.56=.0384 square yardsArea =3.14 \times2.56 =.0384\, square\, yards

STEP 8

The problem asks us to round our answer to the nearest hundredth, so we round8.0384 to8.04.
The area of the rug is8.04 square yards.

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