Question

Can help me complete this problem please :c

Answer 1

112.5 deg

Explanation:

First we find the area of the entire circle.

A = pi * r^2

A = pi * (4 m)^2

A = 16pi m^2

The entire circle has area = 16pi m^2.

The sector has area 5pi m^2.

Now we find the fraction the area of the sector is of the entire circle.

fraction = (5pi m^2)/(16pi m^2) = 5/16 = 0.3125

The full circle has a central angle of 360 deg, the entire circle.

The measure of the central angle of the arc of the sector is the same fraction of the entire circle.

measure of sector angle = 0.3125 * 360 deg = 112.5 deg

Answer 2

The angle is ∅ = 2 radians

Explanation:

The area of a sector of a circle is ½ r² ∅, where r is the radius and ∅ the angle in radians subtended by the arc at the center of the circle.

So arranging the equation for Angle we will get

∅ = 2A/r²

So in the given diagram, by putting the values we get

∅ = 2A/r²

∅ = 2x5(3.14)/4²

∅ = 31.4/16

∅ = 2 radians