A piece of pie with a radius of 14 cm has a central angle of 59°. What is the arc length of the remaining pie's outer edge, to the nearest whole number?

A piece of pie with a radius of 14 cm has a central angle of 59°. What is the arc length of the remaining pie's outer edge, to the nearest whole number?

• A. 70 cm
• B. 74 cm
• C. 80 cm
• D. 76 cm

Answer: (B)

To find the arc length of a piece of pie (which is a sector of a circle), we can use the formula for the arc length, which is given by: \[ \text{Arc Length} = \frac{\theta}{360} \times 2\pi r \] where \( \theta \) is the central angle in degrees and \( r \) is the radius of the circle. In this problem, the radius \( r \) is 14 cm, and the central angle \( \theta \) is 59°. Plugging these values into the formula, we first calculate the circumference of the entire circle: \[ C = 2\pi r = 2\pi \times 14 = 28\pi \text{ cm} \] Now, we find the length of the arc that corresponds to the central angle of 59°: \[ \text{Arc Length} = \frac{59}{360} \times 28\pi \] Next, we can simplify this calculation: \[ \frac{59}{360} \times 28\pi \approx \frac{59 \times 28}{360} \times 3.14 \approx \

To find the arc length of a piece of pie (which is a sector of a circle), we can use the formula for the arc length, which is given by:

[

\text{Arc Length} = \frac{\theta}{360} \times 2\pi r

]

where ( \theta ) is the central angle in degrees and ( r ) is the radius of the circle.

In this problem, the radius ( r ) is 14 cm, and the central angle ( \theta ) is 59°. Plugging these values into the formula, we first calculate the circumference of the entire circle:

[

C = 2\pi r = 2\pi \times 14 = 28\pi \text{ cm}

]

Now, we find the length of the arc that corresponds to the central angle of 59°:

[

\text{Arc Length} = \frac{59}{360} \times 28\pi

]

Next, we can simplify this calculation:

[

\frac{59}{360} \times 28\pi \approx \frac{59 \times 28}{360} \times 3.14 \approx \