Answer:
Part A
The circumference of the circular pie before the slice was cut out is approximately 69.1 inches
Part B; The area of the circular pie before the slice was cut out is approximately 380 in.²
Part C
The area of the slice of pie that was cut out in approximately 40 in.²
Part D;
The length of the crust for the slice of pie is approximately 7 inches
Step-by-step explanation:
Part A
The shape of the pie = Circular shape
The radius of the pie, r = 11 inches
The circumference of a circle = 2·π·r
Therefore, we have;
The circumference of the circular pie before the slice was cut out, 'C', is given as follows;
Where;
r = 2 inches
C = 2 × π × 11 inches = 22·π inches ≈ 69.115 inches
The initial circumference of the circular, C ≈ 69.115 inches
To the nearest tenth of an inch, we have;
The initial circumference of the circular, C ≈ 69.1 inches
Part B; The area of a circle, A = π·r²
Therefore;
For the circular pie before the slice was cut out, A = π·(11 in.)² ≈ 380.133 in.²
To the nearest square inch, we have;
The area of the circular pie before the slice was cut out, A ≈ 380 in.²
Part C
The area of the slice of the pie that was cut out, A is given by the area of a sector of a circle as follows;
[tex]The \ area \ of \ a \ sector, A = \dfrac{\theta}{360 ^{\circ}} \times \pi \cdot r^2[/tex]
The angle of the sector formed by the slice of pie that was cut out, θ = 38°
Therefore, the area of the slice of pie that was cut out, 'A', to the nearest tenth of a square inch is given as follows;
A = 38/360 × π × (11 in.²) = 40 in.²
The area of the slice of pie that was cut out, A = 40 in.²
Part D;
The length of the crust of the slice of pie that was cut out is given by the arc length of the sector of the circular pie the slice of pie represent as follows;
[tex]Arc \ length = \dfrac{\theta}{360 ^{\circ}} \times 2\cdot \pi \cdot r[/tex]
Therefore for the slice of pie, to the nearest inch, we have;
[tex]Arc \ length = \dfrac{38 ^{\circ}}{360 ^{\circ}} \times 2\times \pi \times 11 \, in. \approx 7 \, in.[/tex]
The length of the crust for the slice of pie ≈ 7 in.
