Final answer:
The area of a sector with a radius of 10.5 cm and a central angle of 122 degrees is approximately 368.54 cm^2.
Step-by-step explanation:
The area of a sector of a circle can be found using the formula A = ⅑ × π × r^2, where A is the area of the sector, 1c1 is the central angle in degrees, π is approximately 3.1415927, and r is the radius. For a sector with a radius of 10.5 cm and a central angle of 122 degrees, the calculation would be as follows:
- Convert the central angle from degrees to radians by multiplying by (π/180), since there are 180 degrees in π radians.
- Use the formula to calculate the area.
Step 1: Convert degrees to radians
122 degrees × (π/180) = 2.129301687 radians.
Step 2: Calculate the area
A = ⅑ × π × r^2
= ⅑ × 3.1415927 × (10.5 cm)^2
= (2.129301687/2) × 3.1415927 × 110.25 cm^2
= 1.0646508435 × 346.3605917 cm^2
= 368.535726 cm^2
Therefore, the area of the sector is approximately 368.54 cm^2 after rounding to two decimal places.