What is the area of the sector cut out by two rays in a disc with a given area?

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In summary, the formula for finding the area of a sector is A = (θ/360)πr², the central angle of a sector can be found by dividing the sector's arc length by the circumference of the circle and then multiplying by 360 degrees, you can find the area of a sector without knowing the central angle by using the formula A = (1/2)πr², the area of a sector is a portion of the area of a circle, and finding the area of a sector has real-life applications in various fields such as engineering, architecture, and physics.
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r0bHadz
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Homework Statement


Let Rpq be a ray:

.-------.---------------->
p q

draw a second ray Rpm s.t the angle <QPM has 60 degrees

Let D be a disc centered at P and assume its area is 60 in^2. find the area of the sector in the disc cut out by the two rays

Homework Equations

The Attempt at a Solution


I got 10 in^2 my book is telling me 1 in^2.
 
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  • #2
Book seems wrong. A 60 degree wedge should have 1/6 the area of the circle.
 
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1. What is the formula for finding the area of a sector?

The formula for finding the area of a sector is A = (θ/360)πr², where A is the area, θ is the central angle in degrees, and r is the radius of the circle.

2. How do you find the central angle of a sector?

The central angle of a sector can be found by dividing the sector's arc length by the circumference of the circle and then multiplying by 360 degrees.

3. Can you find the area of a sector without knowing the central angle?

Yes, you can find the area of a sector without knowing the central angle by using the formula A = (1/2)πr², where r is the radius of the circle.

4. How is the area of a sector different from the area of a circle?

The area of a sector is a portion of the area of a circle, determined by the central angle. The area of a circle is the total area enclosed by the circumference.

5. Are there any real-life applications for finding the area of a sector?

Yes, finding the area of a sector is a useful skill in fields such as engineering, architecture, and physics. It can be used to calculate the area of a slice of pizza, the area covered by a sprinkler system, or the area of a component in a circuit diagram.

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