Question

Mom baked a Dutch apple pie in a 9-inch pie pan. She cut the pie into 6 equal pies so that

Answer 1

The area and arc length of each piece can be found using the

relationship between a circle and a sector of the circle.

Responses (b, c, and d are approximated):

a. 120°

b. 10.6 square inch

c. 28.3 in.

d. Area: 15.8 in.², Central angle: 89.1°

How can the pie pieces dimensions be evaluated?

Given:

Diameter of the pan, d = 9-inch

Number pie pieces cut from the apple pie = 6

The pie pieces are sectors of a circular pie.

a. The central angle of one pie pieces = $\dfrac{360^{\circ}}{6}$ = 60°

Therefore;

• The central angle of two pie pieces = 2 × 60° = 120°

b. Area of circular pie = π·r²

Where;

$r = \mathbf{\dfrac{d}{2}}$

Therefore;

$r = \dfrac{9}{2} = \mathbf{ 4.5}$

$The \ area \ covered \ by \ each \ pie \ piece = \dfrac{\pi \times 4.5^2}{6} \approx \mathbf{10.6}$

• The area covered by each pie piece is approximately 10.6 square inch

c. The circumference of a circle = 2·π·r

The circumference of the original pie = 2 × π × 4.5 in. ≈ 28.3 in.

d. Let the arc length of the pie piece = 7 inches

$\mathbf{Area} \ of \ the \ \mathbf{pie \ piece}= \dfrac{7}{2 \cdot \pi \cdot 4.5} \times \pi \times 4.5^2 = \dfrac{7}{2 } \times 4.5 = 15.75 \approx 15.8$

• The area of the pie piece is approximately 15.8 in.²

$The \ central \ angle \ of \ the \ pie \ piece = \dfrac{7}{2 \cdot \pi \cdot 4.5} \times 360^{\circ} \approx \underline{ 89.1^{\circ}}$

Learn more about circumference, area and sector of a circle here:

brainly.com/question/12985985