Math

QuestionFind the area of a circle with a circumference of 14.444 inches. Use π3.14\pi \approx 3.14 and round to the nearest hundredth.

Studdy Solution

STEP 1

Assumptions1. The circumference of the circle is14.444 inches. We are using3.14 as the value of π\pi
3. The formula for the circumference of a circle is C=πrC =\pi r, where CC is the circumference and rr is the radius4. The formula for the area of a circle is A = \pi r^, where AA is the area and rr is the radius

STEP 2

First, we need to find the radius of the circle. We can do this by rearranging the formula for the circumference of a circle to solve for rr.
r=C2πr = \frac{C}{2\pi}

STEP 3

Now, plug in the given values for the circumference and π\pi to calculate the radius.
r=14.4442×3.14r = \frac{14.444}{2 \times3.14}

STEP 4

Calculate the radius.
r=14.4446.28=2.3inchesr = \frac{14.444}{6.28} =2.3\, inches

STEP 5

Now that we have the radius, we can find the area of the circle using the formula for the area of a circle.
A=πr2A = \pi r^2

STEP 6

Plug in the values for π\pi and the radius to calculate the area.
A=3.14×(2.3)2A =3.14 \times (2.3)^2

STEP 7

Calculate the area.
A=3.14×5.29=16.61squareinchesA =3.14 \times5.29 =16.61\, square\, inchesThe area of the circle is16.61 square inches.

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