Question

A circle has a radius of 6 centimeters. What is the area of the sector formed by a central angle measuring 2.4 radians? Enter your answer, as a decimal, in the box.

Answer 1

Area of a circle can be calculated using the following formula
Area = πr²
where π = 3.14 and r - radius of circle
Area of the whole circle is for a central angle of 360°.
We are asked to find the area of a sector. Sector is when 2 arms enclose a central angle by which one arm has rotated.
1 radian = 57.3°
2.4 radian = 57.3 x 2 = 137.52°
Area for 360° = πr²
area for 137.52° = πr² / 360° x 137.52 = π x 6 cm x 6 cm x 0.382 = 13.752 cm²