Question

What is the area of a sector with measure of arc equal to 90Á and radius equal to 1 foot? 0.25pi sq. ft. 0.5pi sq. ft. pi sq. ft

Answer 1

The area of any sector of a circle can be calculated by multiplying the area of the circle and the angle in degrees over 360. It is expressed as:

Area of a sector = πr²(n/360)

We calculate as follows:


Area of a sector = πr²(n/360)

Area of a sector = π(1²)(90/360)

Area of a sector = 0.25π ft² -----> OPTION 1

Answer 2

Given a circle with radius r = 8 and a sector with subtended angle measuring 45°, find the area of the sector and the arc length.

They've given me the radius and the central angle, so I can just plug into the formulas. For convenience, I'll first convert "45°" to the corresponding radian value of π/4:

A = ((pi/4)/2)(8^2) = (pi/8)(8^2) = 8pi, s = (pi/4)(8) = 2pi

area A = 8π, arc-length s = 2π
Given a sector with radius r = 3 and a corresponding arc length of 5π, find the area of the sector.


For this exercise, they've given me the radius and arc length. From this, I can work backwards to find the subtended angle.
Then I can plug-n-chug to find the sector area.
5pi = (theta)(3), (theta) = (5/3)pi So the central angle is (5/3)π.
Then the area of the sector is:
A = ((5/3)pi / 2)*(3^2) = ((5/6)pi)*(9) = (15/2)pi A = (15 pi) / 2

90/360 = 0.25 pi sq ft