A sector of a circle has an arc measurement of 110°. The area of the sector is 11兀 cm2. What is the diameter of the circle?
To find the diameter of the circle, we need to first find the radius of the circle using the given information about the sector.
The formula for the area of a sector of a circle is:
Area of sector = (θ/360) * π * r^2
Where θ is the central angle of the sector in degrees, r is the radius of the circle, and π is a constant approximately equal to 3.14159.
Given that the area of the sector is 11兀 cm^2 and the central angle is 110°, we can plug these values into the formula and solve for the radius:
11兀 = (110/360) * π * r^2
11兀 = 0.3056 * 3.14159 * r^2
11兀 = 0.960788 * r^2
r^2 = 11兀 / 0.960788
r^2 ≈ 11.441 cm^2
r ≈ 3.38 cm
Now that we have the radius of the circle, we can find the diameter by multiplying the radius by 2:
Diameter = 2 * 3.38 cm
Diameter ≈ 6.76 cm
Therefore, the diameter of the circle is approximately 6.76 cm.