Problema Solution
A sector of a circle is enclosed by two 12-inch radii and a 9-inch arc. It's perimeter is therefore 33 inches.
a) What is the central angle of the sector, to the nearest tenth of a degree?
b) What is the area of this sector, to the nearest tenth of a square inch?
Answer provided by our tutors
let
r = 12 in the radii
l = 9 in the length of the arc
P = 33 in the length of the sector
a) What is the central angle of the sector, to the nearest tenth of a degree?
central angle = 2pi*(l/(2*r*pi)) (since 360 degrees = 2pi radians)
central angle = 2pi*(9/(2*12*pi)
central angle = 0.75 radians
central angle = 0.75*360/2pi degrees
central angle = 42.99 degrees
b) What is the area of this sector, to the nearest tenth of a square inch?
A = r^2*pi*(0.75/2pi)
A = 12*2*pi*0.75/2pi
A = 9 in^2