MHB What is the formula for finding the area of a circle?

  • Thread starter Thread starter mathland
  • Start date Start date
  • Tags Tags
    Area Circle
Click For Summary
The discussion centers on finding the area of a circle using the formula A = πr². The user initially miscalculates the radius by incorrectly relating the diameter to the circumference. They clarify that the diameter is 10, not 10π, leading to the correct calculation of the radius as 5. The error in cubing π in the area calculation is acknowledged, emphasizing that the area should not involve volume. The thread concludes with the user recognizing their mistake and expressing gratitude for the correction.
mathland
Messages
33
Reaction score
0
FB_IMG_1611801510361.jpg


My Effort:

Circumference = pi•d

10 •pi = pi•d

10•pi/pi = d

10 = d, where d is the diameter of the circle.

Area = pi•r^2, where r is the radius of the circle.

Diameter = 2 times the radius.

10pi = 2r

10pi/2 = r

5pi = r

A = pi•r^2

A = pi(5pi)^2

A = 25•pi^3, which makes no sense.

Only the volume is cubed. This is not a volume question.
 
Mathematics news on Phys.org
mathland said:
Circumference = pi•d
10 •pi = pi•d
10•pi/pi = d
10 = d[/color], where d is the diameter of the circle. Correct![/color]
Area = pi•r^2, where r is the radius of the circle.
Diameter = 2 times the radius.
10pi[/color] = 2r Wrong![/color]
The diameter is 10, not 10pi.
 
Opalg said:
The diameter is 10, not 10pi.

I see my error. Thanks.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

MHB ASVAB circle and inscribed rectangle area problem
  • · Replies 6 ·
Replies
6
Views
2K
High School Understanding why πr^2 works for different area calculations
  • · Replies 7 ·
Replies
7
Views
2K
High School Area of a Circle in an Electron's Hydrogen Atom
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Average chord length of a circle
  • · Replies 7 ·
Replies
7
Views
10K
MHB How Much Should the Radius Increase to Enlarge the Circle's Area by b Units?
  • · Replies 4 ·
Replies
4
Views
2K
MHB The height of a section of overlapping circles.
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Finding Minimal Mean Distance Curves on the Unit Sphere
  • · Replies 2 ·
Replies
2
Views
2K
MHB Find the exact shaded area of the region in 4 overlapping circles
  • · Replies 1 ·
Replies
1
Views
3K
High School Integrating to find surface area/volume of hemisphere
  • · Replies 3 ·
Replies
3
Views
3K
MHB Explaining the Area of a Circle: Understanding A(r) = πr^2
  • · Replies 4 ·
Replies
4
Views
4K