Question

In the following questions, the radius of circle O is given, as well as the measure of central angle AOB. Find the area of the segment of circle O bounded by AB and AB . Give exact values whenever possible. Otherwise, round answers to the nearest hundredth.Radius: 7 inCentral Angle: 4π/5A. 370.4 in2

B. 81.4 in2
C. 47.2 in2
D. 32.8 in2
E. 320.8 in2
F. None of these

Answer 1

OPTION B.

To find the area of the segment of circle O bounded by AB and AB, we can use the formula for the area of a segment and substitute the given values of the radius and central angle.

Step-by-step explanation:

To find the area of the segment of circle O bounded by AB and AB, we can use the formula for the area of a segment:

Area = (θ/360°) × πr² - (1/2) × r² × sin(θ)

Given the radius of circle O is 7 in and the measure of central angle AOB is 4π/5, we can substitute these values into the formula.

Area = (4π/5/360°) × π(7 in)² - (1/2) × (7 in)² × sin(4π/5)

After calculating, we find that the area of the segment is approximately 81.4 in², so the correct answer is B.

Answer 2

C.47.2 square in

Step-by-step explanation:

We are given that

Radius,r=7 in

Central angle,
`\theta=(4\pi)/(5)`rad

We have to find the area of segment of circle O.

Area of segment=Area of sector-Area of triangle

Area of triangle=
`=(1)/(2)* base* height=(1)/(2)* 7^2sin((4\pi)/(5))=14.4in^2`

Area of sector=
`(\theta)/(2\pi)* \pi r^2=(4\pi)/(10\pi)* \pi (7)^2=61.57 in^2`

Area of segment=(61.57-14.4)square in

Area of segment=47.17 square in
`\approx 47.2in^2`

Hence, option C is true.