Find the area of sector in a circle in terms of pi. (Geometry)

In summary, a sector in a circle is a region bounded by two radii and an arc of the circle, similar to a slice of pizza. To find its area, you can use the formula A = (θ/360)πr², where θ is the central angle and r is the radius. The value of π used in this formula is the same as the value used for finding the area of a circle. The area of a sector can be expressed in terms of π and is always a positive value. It cannot be negative.
  • #1
Etrujillo
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View attachment 8699

So far i have 270/360× (pi)r^ i don't know what to do next please help.
 

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  • #2
I would first reduce:

\(\displaystyle \frac{270^{\circ}}{360^{\circ}}=\frac{3}{4}\)

And so we now have the area \(A\):

\(\displaystyle A=\frac{3}{4}\pi r^2\)

Can you identify the radius \(r\) of the circle from the diagram?
 
  • #3
The radius i believe is 12m so when i plug in your formula i get 108pi as the answer. Am i correct?
 
  • #4
Yes, [tex]108\pi[/tex] is correct.
 

FAQ: Find the area of sector in a circle in terms of pi. (Geometry)

What is a sector in a circle?

A sector in a circle is a region bounded by two radii and an arc of the circle. It is similar to a slice of pizza, with the radii acting as the crust and the arc as the toppings.

How do you find the area of a sector in a circle?

To find the area of a sector in a circle, you can use the formula A = (θ/360)πr², where θ is the central angle of the sector and r is the radius of the circle. This formula uses the fact that the area of a whole circle is πr², and the ratio of the central angle θ to the full angle of 360 degrees is the fraction of the circle's area that the sector covers.

What is the value of π for finding the area of a sector?

The value of π used in finding the area of a sector is the same as the value used for finding the area of a circle, which is approximately 3.14159. It is a constant value that represents the ratio of a circle's circumference to its diameter.

Can the area of a sector be expressed in terms of π?

Yes, the area of a sector can be expressed in terms of π. In fact, the formula for finding the area of a sector (A = (θ/360)πr²) already includes π. This means that you can leave the answer in terms of π without having to calculate its decimal approximation.

Can the area of a sector be negative?

No, the area of a sector cannot be negative. It is always a positive value, as it represents the amount of space covered by the sector within the circle. If the calculated area is negative, it means that there was an error in the calculations or that the central angle was incorrectly measured.

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