Question

find the circumference of the circle. give the exact circumference and then an approximation. use π ≈ 3.14. the exact circumference of the circle is (simplify your answer. type an exact answer in terms of π.) the approximate circumference of the circle is (type a whole number or a decimal rounded to the nearest hundredth.)

Explanation:

Step1: Recall the formula for the circumference of a circle.

The formula for the circumference \( C \) of a circle is \( C = 2\pi r \), where \( r \) is the radius of the circle. From the diagram, the radius \( r = 5 \) m.

Step2: Calculate the exact circumference.

Substitute \( r = 5 \) into the formula: \( C = 2\pi \times 5 = 10\pi \) meters.

Step3: Calculate the approximate circumference.

We know that \( \pi \approx 3.14 \), so substitute \( \pi \approx 3.14 \) and \( r = 5 \) into the formula \( C = 2\pi r \). First, \( 2\times3.14\times5 \). Calculate \( 2\times5 = 10 \), then \( 10\times3.14 = 31.4 \) meters.

Answer:

The exact circumference of the circle is \( 10\pi \) meters.
The approximate circumference of the circle is \( 31.4 \) meters.