What's the length of the arc ab and the area of the sector aob
If angle θ subtends arc ab on a circle of radius r,
arc ab = rθ
area = 1/2 r^2 θ
To find the length of the arc AB and the area of the sector AOB, we need to know three things: the radius of the circle (r), the central angle (θ) in radians (measured at the center of the circle), and the circumference of the circle (C).
1. Length of the Arc AB:
The formula to find the length of an arc is given by the formula:
Arc Length (AB) = (θ/2π) * C
To calculate the length of the arc AB, you need to know the central angle θ and the circumference C of the circle. The central angle θ is usually given in degrees, so you'll need to convert it to radians by multiplying it by (π/180).
2. Area of the Sector AOB:
The formula to find the area of a sector is given by:
Area (AOB) = (θ/2π) * π * r^2
where r is the radius of the circle and θ is the central angle in radians.
To find the area of the sector AOB, you need to know the central angle θ and the radius r of the circle.
Remember, if the central angle is given in degrees, convert it to radians before using these formulas by multiplying it by (π/180).