The area of a circle is πr2. To find the area of a sector with a central angle of Θ, measured in radians, by what should you multiply πr2?
A) Θ
B) 2Θ
C) Θ/2
D) Θ/2π
is the answer D
still yes
Yes, the correct answer is D) Θ/2π.
To find the area of a sector, you can multiply the area of the whole circle (πr^2) by the fraction of the angle that the sector occupies.
In this case, the central angle of the sector is given as Θ, measured in radians. The entire circle has a central angle of 2π radians, which is equivalent to 360 degrees.
So, to find the fraction of the angle that the sector occupies, you divide Θ by 2π. This fraction represents the ratio of the angle of the sector to the full circle angle.
Finally, you multiply this fraction by the area of the whole circle (πr^2). So, the formula for finding the area of a sector is:
Area of sector = (Θ/2π) * πr^2
Simplifying the equation, π cancels out:
Area of sector = (Θ/2) * r^2
Therefore, the correct answer is D) Θ/2π.