Question

A circle has a radius of 2.5 centimeters and a central angle AOB that measures 90°. What is the area of sector AOB? Use 3.14 for pi and round your answer to the nearest tenth.
A. 2.9 cm2
B. 3.9 cm2
C. 4.9 cm2
D. 19.6 cm2

Answer 1

The area of any circle is        (pi) x (radius)²  .

The area of the WHOLE circle in the question is

                                                 (pi) x (2.5 cm)²

                                             =  (pi) x (6.25 cm²) .

The full circle is made by 360° of central angles.

90° of central angle makes a pie-wedge (sector)
that's exactly one fourth of the circle, so its area
is one fourth of the area of the whole circle.

                     Area = (1/4) (pi) (6.25 cm²)

                               = (0.25) (3.14) (6.25 cm²)

                               =    4.906 cm² .

Rounded to the nearest tenth:   4.9 cm² .