Question

The central angle of a sector of a circle having diameter 12 cm measures 75°. Find the following (keeping π in the answers): (a) the length, s, of the intercepted arc (b) the area, A, of the sector.

a) (3π) cm, (15/8π , cm²)
b) (2π) cm, (9/4π , cm²)
c) (4π) cm, (21/8π , cm²)
d) (5π) cm, (27/4π , cm²)

Answer 1

The length of the intercepted arc is (15/8π) cm and the area of the sector is (9/4π) cm².

Step-by-step explanation:

The length of the intercepted arc can be found using the formula:
s = (θ/360°) × 2πr
Where θ is the measure of the central angle, and r is the radius of the circle. In this case, the central angle is 75° and the diameter is 12 cm. Therefore, the radius (r) is half the diameter (r = 6 cm).
Substituting these values into the formula:
s = (75/360) × 2π × 6 = 15/8π cm

The area of the sector can be found using the formula:
A = (θ/360°) × πr²
Using the same values as before:
A = (75/360) × π × 6² = 9/4π cm²