Question

Consider the given circle with the shaded sector xy and central angle, 225°. The circumference of the circle is 30 units. A circle with center c has two lines cx and cy drawn from the center of the circle to the circle wall such that the exterior angle of xcy is 225 degrees. Use the given information to complete the statements. Round any non-integer answers to the hundredths place. The length of major arc xy is _______ units. The radius of the circle is _______ units. The area of the shaded sector is _______ square units.

Answer 1

The length of major arc xy is 18.75 units. The radius of the circle is 4.77 units. The area of the shaded sector is 43.48 square units.

Step-by-step explanation:

Given that the central angle of sector xy is 225° and the circumference of the circle is 30 units, we can find the length of major arc xy using the formula:

Length of arc = (central angle/360°) x circumference

Therefore, Length of arc xy = (225°/360°) x 30 = 18.75 units

To find the radius of the circle, we can use the formula:

Radius = Circumference / (2π)

Therefore, Radius = 30 / (2π) ≈ 4.77 units (rounded to the hundredths place)

To find the area of the shaded sector xy, we can use the formula:

Area = (central angle/360°) x π x (radius)^2

Therefore, Area of sector xy = (225°/360°) x π x (4.77)^2 ≈ 43.48 square units (rounded to the hundredths place)