Find the area of a sector with a central angle of 170° and a diameter of 9.1 cm. Round to the nearest tenth.
A. 122.9 cm2
B. 30.7 cm2
C. 8.6 cm2
D. 3.4 cm2
The area of the circle is calculated through the equation, A = πr² where A is the area and r is the radius. An alternate equation can be used, A = πD²/4 where D is the diameter.
Substituting the known value to the equation, A = π(9.1 cm)² / 4 A = 65.03 cm²
The area of the sector, As, is calculated by multiplying the area of the circle by the ratio of the angle to the whole revolution. As = (65.03 cm²) x (170°/360°) As = 30.71 cm²
The answer to this question is therefore letter B.
