Final answer:
The length of the crust of a pie slice with a radius of 4 inches and a central angle of 47° is determined by finding the portion of the circle's circumference that this angle represents. The crust length is approximately 2.61 inches.
Step-by-step explanation:
The student is asking to find the length of the crust of a slice of pie with a radius of 4 inches and a central angle of 47°. To find the length of the arc (crust), we use the formula for the circumference of a circle (C = 2πr) and adjust it for the portion of the circle defined by the central angle. The circumference of the full circle would be 2π×(4 inches), but we only need the length corresponding to 47° of the full 360° of the circle.
To find the length of the arc (L), the calculation is as follows:
- Determine the fraction of the circle the angle represents: °/360°.
- Multiply the fraction by the full circumference of the circle: (Fraction) × 2πr.
- Plug in the values: (47°/360°) × 2π×(4 inches).
Calculating this we get:
L = (47/360) × 2π×(4 inches) ≈ 2.61 inches
So, the length of the crust of the slice is approximately 2.61 inches.