Find the measure of the central angle, in radians, given the area of the sector as
22.6 cm2 and a radius equal to 3.7 cm
total area = pi r^2 = pi(3.7*2) = 43
22.6/43 = .5255
.5255 *2 pi = 3.3 radians
To find the measure of the central angle in radians, we can use the formula for the area of a sector:
Area = (θ/2) * r^2
where θ is the central angle in radians and r is the radius.
First, let's rearrange the formula to solve for θ:
θ = (2 * Area) / r^2
Now we can substitute the given values into the formula:
θ = (2 * 22.6 cm^2) / (3.7 cm)^2
Simplifying the equation:
θ = (2 * 22.6) / (3.7)^2
θ = 45.2 / 13.69
θ ≈ 3.30 radians
Therefore, the measure of the central angle is approximately 3.30 radians.