A circle has a general formula for area as:
A = (θ / 360°) * π * r^2
So when we are to look for the area of the circle, the θ
= 360° and the factor (θ / 360°) is simply equals to 1 and is removed from the
formula. However in this case, we are to find for the area of a portion of a
circle, specifically a sector.
It is given that the radius is 6 m and the central angle
intercepted by this sector is 3 / 4 radians. As we can see in the formula, the
angle θ is expressed in degrees, therefore we need to convert the central angle
first into degrees.
Central angle θ = (3 / 4 rad) (180° / π rad)
Central angle θ = (135/π)°
So the area of the sector is:
A sector = (135/π / 360) * π *
(6 m)^2
A sector = 13.5 m^2
