Math  /  Geometry

QuestionThe circumference of a circle is 8.164 kilometers. What is the circle's Use π3.14\pi \approx 3.14 and round your answer to the nearest hundredth. \square square kilometers Submit

Studdy Solution

STEP 1

1. The circle's circumference is given as 8.164 8.164 kilometers.
2. Use π3.14\pi \approx 3.14.

STEP 2

1. Recall the formula for the circumference of a circle.
2. Solve for the radius.
3. Recall the formula for the area of a circle.
4. Substitute the radius into the area formula.
5. Calculate the area and round to the nearest hundredth.

STEP 3

Recall the formula for the circumference of a circle:
C=2πr C = 2\pi r
where C C is the circumference and r r is the radius.

STEP 4

Solve for the radius r r using the given circumference:
8.164=2×3.14×r 8.164 = 2 \times 3.14 \times r
Divide both sides by 2×3.14 2 \times 3.14 :
r=8.1642×3.14 r = \frac{8.164}{2 \times 3.14}
Calculate r r :
r8.1646.281.3 r \approx \frac{8.164}{6.28} \approx 1.3

STEP 5

Recall the formula for the area of a circle:
A=πr2 A = \pi r^2

STEP 6

Substitute the radius into the area formula:
A=3.14×(1.3)2 A = 3.14 \times (1.3)^2

STEP 7

Calculate the area and round to the nearest hundredth:
A3.14×1.69 A \approx 3.14 \times 1.69 A5.3066 A \approx 5.3066
Rounded to the nearest hundredth:
A5.31 A \approx 5.31
The area of the circle is:
5.31 square kilometers \boxed{5.31} \text{ square kilometers}

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