if the area of ​​a circle sector is 80. square feet and the radius of the circle is 4 feet, find the sector angle in radians to the nearest hundredth

Question

Plz help :( its precalculus homework that my professor doesnt explain

Answer 1

Given: Area of a circle sector is 80 ft^2 and radius = 4 ft

Find: Sector angle in radians to the nearest hundreth.

Solution:

Area of whole circle = pi*r^2

Area of whole circle = pi*(4)^2 = 16*pi ~ 50.3 ft^2

NOTE: The area of the sector is greater than the area of the circle.

Either the given information is wrong

or the sector is greater than 2pi radians (or 360 degrees)

Sector is part of the whole circle.

(80) / (16*pi) is the sector part of the circle.

There are 2pi radians in a whole circle.

Let x = degrees of sector in radians

Setup a proportion.

80 / (16*pi) = x / (2*pi) Multiply both sides by pi

80 / (16) = x / (2)

160 / 16 = x

10 = x

The sector is 10.00 radians

Extra: Convert to degrees

10 * (180/pi) = 572.96 degrees

NOTE: A sector greater than 360 degrees

was predicted, with the given information.