Question

Consider the given circle with the shaded sector XY and central angle, 225°. The circumference of the circle is 30 units.

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

XY ≈ 58.90

r = 15

Area of the shaded sector = 441.79

Explanation:

Find the radius using circle circumference formula:

2πr = 30π

r = 30/2 = 15

Use the radius to find the arc length:
XY = 2πr*225/360 = 2π(15)*225/360 ≈ 58.9

Calculate the sector area:

πr^2 *225/360 = π*(15)^2 *225/360 ≈ 441.79