A sector of a circle has an arc measurement of 110°. The area of the sector is 11z cm'. What is the diameter of the circle?
To find the diameter of the circle, we first need to find the radius of the circle using the given information.
The area of a sector of a circle is calculated using the formula:
Area of sector = (θ/360) x πr^2
where θ is the arc measurement in degrees, r is the radius of the circle, and π is approximately 3.14159.
Given that the area of the sector is 11z cm² and the arc measurement is 110°, we can plug these values into the formula:
11z = (110/360) x πr^2
11z = 0.3056πr^2
Now, we need to find the value of πr^2:
πr^2 = 11z / 0.3056
πr^2 = 35.995 lt;z
r^2 = 35.995 / π
r^2 = 11.44
r ≈ √11.44
r ≈ 3.38
Now that we have found the radius of the circle to be approximately 3.38 cm, we can find the diameter of the circle:
Diameter = 2 x radius
Diameter = 2 x 3.38
Diameter ≈ 6.76
Therefore, the diameter of the circle is approximately 6.76 cm.