Question

Mom baked a Dutch apple pie in a 9-inch pie pan. She cut the pie into 6 equal pies so that
everyone gets the same sized piece.
a. Determine the central angle created by two pieces of pie.
b. Determine the area covered by each piece of pie to the nearest tenth of a square inch.
c. Determine the circumference of the original pie to the nearest tenth of an inch.
9
d. If a piece of pie had an arc length of g7, determine the area of the piece of pie to the
nearest tenth of a square inch. What would be the central angle of this piece of pie?

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:

https://brainly.com/question/12985985