Find the area of the sector of a circle of radius 14 units subtended by an angle of 23π12 radians. Round your answer to the nearest tenth, and do not include the units in your answer.

Question

Help me please! I have been stuck on this one question for so long:

Find the area of the sector of a circle of radius 14 units subtended by an angle of 23π12 radians. Round your answer to the nearest tenth, and do not include the units in your answer.

Answer 1

23pi/12 is almost 24pi/12 = 2pi which is the full circle, just pi/12 less. pi/12 = 15 degrees

23pi/12 = 345 degrees. A full circle is 360 degrees

Area of a circle with radius 14 is pi(r)^2 = pi(14)^2 = 196pi = about 615.8

Area of a sector with 345 degrees is 345/360 x 196pi= 23/24 x 196pi =

23x49/6 x pi = 1127pi/6 = about 187.8333(3.14159) = about 590.1

Area of the sector = 590.1 rounded to one decimal place

(this all assumes you meant 23pi/12 when you wrote "23pi12" Odds are you left out "/" between the pi and 12)

Answer 2

The area of an entire circle is π•r²

Since there are 2π radians in the whole circle, we can just set up a proportion:

A_sector = Angle_sector/(2π)•π•r²

So:

A_sector = (23π/12)/(2π)(π•14²)

A_sector = (23/24)(π•14²)

A_sector = (23/24)(π•196) = 4508π/24 = 1127π/6 ≈ 590.1