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?

Answer 1

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.