If radius and perimeter of sector of a circle is 3.4 cm and 12.8 cm respectively,then find the area of sector of a circle
Answers
Answer:
Step-by-step explanation:
The perimeter of a sector of a circle with a radius of 6.5 cm is 23.4 cm. What is the area of the sector?
The perimeter of a sector of a circle with a radius of 6.5 cm is 23.4 cm. So the length of the arc of the sector is 23.4 - 2*6.5 = 23.4–13.0 = 10.4 cm.
The circumference of the circle of radius 6.5 cm is 2(pi)*6.5 = (2*22*6.5/7) = 40.85714286 cm.
The ratio of the arc length to the circumference is 10.4 : 40.85714286.
The area of the sector to the area of the circle will be in the same ratio of the arc length to the circumference.
10.4 : 40.85714286 ::area of sector : area of circle, or
10.4 : 40.85714286 ::area of sector : (pi)*6.5^2, or
10.4 : 40.85714286 ::area of sector : 132.7857143, or
Area of sector = 10.4 * 132.7857143/40.85714286
= 33.8 sq cm