The area of a sector of a circle is 40cm2.If the radius 𝑟=5cm, what is the value of the central angle in radians?
Question
The area of a sector of a circle is 40cm2.If the radius 𝑟=5cm, what is the value of the central angle in radians?
Solution
The area of a sector of a circle is given by the formula:
Area = 0.5 * r² * θ
where r is the radius and θ is the central angle in radians.
We are given that the area is 40 cm² and the radius r is 5 cm. We can substitute these values into the formula and solve for θ:
40 = 0.5 * (5)² * θ 40 = 0.5 * 25 * θ 40 = 12.5 * θ
Now, divide both sides by 12.5 to solve for θ:
θ = 40 / 12.5 θ = 3.2 radians
So, the central angle is 3.2 radians.
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