Find the area of the sector of a circle with diameter 30 feet and an angle of 4Pi/3 radians

Answer 1

A = r²(θ / 2), θ in radians

A = 15²(4π/6)

Can you calculate and answer?

Answer 2

diameter = 30 feet

radius = r = d/2 = 30/2 = 15 feet

area of the full circle is pi times the radius squared

= pi(r^2)

= pi(15^2)

= 225pi

the area of a sector with angle 4pi/3 is (4pi/3)/2pi = 2/3 times the area of the full circle

sector area

= (4pi/3)/2pi x 225pi

= 2/3 x 225pi

= 450pi/3

= 150pi ft^2

sector of angle 4pi/3 is over half the the circle. half the circle has angle of pi

area of the sector will be over half the circle's area

150 is over half of 225

think of the full circle as a "sector" with angle 2pi

then 4pi/3 is to 2pi what the area of the sector is to the area of the full circle

they have the same ratio

(4pi/3)/2pi = sector area/full circle area = 2/3

2/3 x 225pi = 150pi square feet

150pi = about 150 x 3.14159. pi=about 3.14159. often rounded to 3.14 or to 22/7

=150(22)/7

=3300/7

= about 471 ft^2