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.
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?
3 answers
so is it 36cm, 12cm, 16cm or 18cm
The correct answer is 12 cm.