a circle with center o has radius of 5cm and angle of 60 degrees.
find the area of the minor sector
find the area of angle aob
find the area of the minor segment
find the length of the arc minor arc i found the area which is 78.54cm
pi =3.14
minor sector: a = 1/2 r^2 θ = 1/2 * 25 * π/3 = 25/6 π
no idea where A and B are, but angles do not have areas.
minor segment: 1/2 r^2 (θ-sinθ) = 1/2 * 25 (π/3 - √3/2)
arc length = rθ = 5 * π/3 = 5/3 π
I see you found the area of the circle, which is πr^2 = 25π = 78.54
To find the area of the minor sector, you can use the formula: (angle/360) * π * r^2, where "angle" is the measure of the angle in degrees, "π" is approximately 3.14, and "r" is the radius of the circle.
In this case, the angle is 60 degrees, and the radius is 5 cm.
Area of the minor sector = (60/360) * 3.14 * 5^2
= (1/6) * 3.14 * 25
≈ 13.09 cm²
To find the area of angle AOB, you can use the formula: (angle/360) * π * r^2.
In this case, the angle is also 60 degrees and the radius is 5 cm.
Area of angle AOB = (60/360) * 3.14 * 5^2
= (1/6) * 3.14 * 25
≈ 13.09 cm²
To find the area of the minor segment, subtract the area of the triangle from the area of the sector.
The area of the triangle can be found using the formula: (1/2) * base * height, where "base" is the length of the chord and "height" is the perpendicular distance between the chord and the center of the circle.
In this case, since the angle is 60 degrees, the triangle formed is an equilateral triangle with base equal to the chord length and height equal to the radius.
Chord length (AB) = 2 * radius * sin(angle/2)
= 2 * 5 * sin(60/2)
= 2 * 5 * sin(30)
= 2 * 5 * (1/2)
= 5 cm
Now, we can find the height of the equilateral triangle which is also the radius of the circle (5 cm).
Area of the triangle = (1/2) * 5 * 5
= 12.5 cm²
Area of the minor segment = Area of the sector - Area of the triangle
= 13.09 - 12.5
≈ 0.59 cm²
Finally, to find the length of the minor arc, you can use the formula: arc length = (angle/360) * 2 * π * r.
In this case, the angle is 60 degrees and the radius is 5 cm.
Length of minor arc = (60/360) * 2 * 3.14 * 5
= (1/6) * 6.28 * 5
= 0.5236 * 5
≈ 2.6 cm