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

Click For Summary
SUMMARY

The area of a sector in a circle can be calculated using the formula \(A = \frac{\theta}{360} \times \pi r^2\), where \(\theta\) is the angle in degrees and \(r\) is the radius. In this discussion, the angle is 270 degrees, which simplifies to \(\frac{3}{4}\) when divided by 360. Given a radius of 12 meters, the area computes to \(A = \frac{3}{4} \pi (12)^2 = 108\pi\) square meters, confirming that the calculation is correct.

PREREQUISITES
  • Understanding of basic geometry concepts, particularly circles and sectors.
  • Familiarity with the formula for the area of a circle.
  • Ability to manipulate fractions and perform basic arithmetic operations.
  • Knowledge of the relationship between degrees and radians in geometry.
NEXT STEPS
  • Study the derivation of the area of a sector formula in more detail.
  • Explore problems involving sectors with different angles and radii.
  • Learn about the relationship between radians and degrees in circular measurements.
  • Investigate applications of sector area calculations in real-world scenarios, such as engineering and architecture.
USEFUL FOR

Students studying geometry, educators teaching mathematical concepts, and anyone interested in applying geometric principles to solve problems involving circles and sectors.

Etrujillo
Messages
9
Reaction score
0
View attachment 8699

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

Attachments

  • 20181204_093323-2.jpg
    20181204_093323-2.jpg
    6.4 KB · Views: 125
Last edited by a moderator:
Mathematics news on Phys.org
I would first reduce:

$$\frac{270^{\circ}}{360^{\circ}}=\frac{3}{4}$$

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

$$A=\frac{3}{4}\pi r^2$$

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

Similar threads

MHB Find the area of the shaded region in terms of pi.
  • · Replies 3 ·
Replies
3
Views
2K
MHB What is the formula for finding the area of a circle?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Find the areas of segment in circle
  • · Replies 1 ·
Replies
1
Views
2K
MHB Find the exact shaded area of the region in 4 overlapping circles
  • · Replies 1 ·
Replies
1
Views
3K
MHB Solving a Primary Math Problem: Find the Areas of A & C
  • · Replies 10 ·
Replies
10
Views
2K
MHB Find the area of the shaded region
  • · Replies 2 ·
Replies
2
Views
1K
High School Area of a Circle in an Electron's Hydrogen Atom
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Equation to graph a sine wave that acts like a point on a unit circle
  • · Replies 8 ·
Replies
8
Views
2K
MHB How to Solve for r and θ in a Circle's Minor Arc and Sector Area Problem?
  • · Replies 7 ·
Replies
7
Views
4K
High School Understanding why πr^2 works for different area calculations
  • · Replies 7 ·
Replies
7
Views
2K