Question

1. if cr = 28 inches, find the length of arc \\(\overarc{bc}\\).
2. a 9 -inch cherry pie is cut into 12 equal slices. find the perimeter of one slice of pie. round to the nearest hundredth.

Explanation:

Problem 6

Step1: Identify radius

CR is diameter, so radius \( r = \frac{28}{2} = 14 \) inches.

Step2: Arc length formula

Arc length \( L = \frac{\theta}{360^\circ} \times 2\pi r \), where \( \theta = 100^\circ \), \( r = 14 \).

Step3: Calculate arc length

\( L = \frac{100^\circ}{360^\circ} \times 2\pi \times 14 \)
\( = \frac{5}{18} \times 28\pi \)
\( = \frac{140\pi}{18} \approx \frac{140 \times 3.1416}{18} \approx 24.43 \) inches.

Step1: Radius of pie

Diameter is 9 inches, so radius \( r = \frac{9}{2} = 4.5 \) inches.

Step2: Arc length of slice

Each slice has central angle \( \theta = \frac{360^\circ}{12} = 30^\circ \).
Arc length \( L = \frac{30^\circ}{360^\circ} \times 2\pi r = \frac{1}{12} \times 2\pi \times 4.5 = \frac{9\pi}{12} = \frac{3\pi}{4} \approx 2.356 \) inches.

Step3: Perimeter of slice

Perimeter = arc length + 2×radius = \( 2.356 + 2 \times 4.5 = 2.356 + 9 = 11.356 \approx 11.36 \) inches.

Answer:

Approximately \( 24.43 \) inches.

Problem 7