find the area of a sector that has a central angle of 68 degrees and a radius of 10cm. Round you answer to the nearest 100th. (use 3.14=pie)
recall that the area
a = 1/2 r^2 θ
Now just convert 68° to radians and plug in your numbers.
To find the area of a sector, you can use the formula:
Area = (θ/360) * π * r^2
where θ is the central angle, π is the value of pi (approximately 3.14), and r is the radius.
In this case, we have a central angle of 68 degrees and a radius of 10 cm.
Plugging in the values:
Area = (68/360) * 3.14 * (10^2)
Calculating:
Area = (0.1889) * 3.14 * (100)
Area = 59.24 cm^2
Rounded to the nearest hundredth, the area of the sector is approximately 59.24 square centimeters.
To find the area of a sector, you can follow these steps:
1. Convert the central angle from degrees to radians. To convert, you can use the formula: radians = (degrees * π) / 180. In this case, we have a central angle of 68 degrees, so the calculation would be: (68 * 3.14) / 180 = 1.191 radians.
2. Use the formula for the area of a sector: area = (r^2 * θ) / 2, where r is the radius and θ is the central angle in radians. Plugging in the values, we have: area = (10^2 * 1.191) / 2 = 59.55 cm^2.
3. Finally, round the answer to the nearest hundredth. In this case, the area of the sector is approximately 59.55 cm^2.