Geometry Circle??

Question

A 36 degree arc of circle C is 24π units long. Circumference and and the area of the circle

Answer 1

Arc length = (m /360)2πr.

Where m is measure of the central angle or arc, and

2πr is the circumference of the entire circle.

• From the given data :

Arc length = 24π units.

measure of the central angle or arc (m) = 36 degrees.

Substitute the values arc length = 24π and m = 36 in Arc length = (m /360)2πr.

24π  = (36 /360)2πr.

Circumference of the circle (2πr) = 24π * (360/36)

= 24π * 10

= 240π.

Circumference of the circle (2πr) = 240π units.

 

• θ = 0.2π radians

radius (r ) = (arc length)/θ.

Substitute the values of arc length = 24π and θ = 0.2π in r  = (arc length)/θ.

r = 24π/(0.2π)

= 120 units
Area of the circle (A) = πr ².

Substitute the values π = 3.14 and r = 120 in A = πr ².

A = (3.14) * (120)²

= 3.14 * 14400

≅ 45,239 square units.

Area of the circle is 45,239 square units.

Answer 2

The formula for the length of the arc = 2πr(C/360), where C  is the central angle of the arc in degrees, r  is the radius of the arc and π  is pi, 22/7 (approximately 3.142).

The formula for the circumference of the circle is 2πr units and the area of the circle is πr².

The angle is 36 degrees and length of the arc 24π units.

Length of the arc = 2πr(C/360).

24π = 2πr(36/360)

240π = 2πr

240(22/7) = 2πr

754.29 ≅ 2πr.

The circumference of the circle is 2πr = 240π and solve for r.

r = 120 units.

The area of the circle is πr² = π(120)² = (22/7)(14400) ≅ 45257 units².

The circumference of the circle is 754.29 units and the area of the circle is 45257 square units.