Calculating area of multiple connected circles

In summary, the conversation discusses a challenging math problem that involves comparing the surface area of four identical circles to that of a single circle overlayed on top of them. The method proposed is to calculate the maximum separation between the circles represented by circle B, with diameter B, and then use 2x + B as the diameter of the overlayed circle. The formula for the surface area of the four circles is 4πx^2/4, which simplifies to πx^2. The conversation also mentions a potentially easier method involving creating a triangle with the centers of the circles.
  • #1
magnetics
Gold Member
47
0
Hopefully this is a challenging maths problem for someone. This problem is to compare the surface area of the 4 identical circles with the circle overlayed drawn in pencil.

The attached image shows 4 circles, each with diameter x.
To solve the problem, I need to calculate the maximum separation between the circles represented by the circle B with diameter B.

Once B can be calculated, 2x + B will be the diameter of a single circle overlayed over the four as shown in pencil.

This seems to me to be the simplest method to compare the difference in surface area between the four circles and the overlayed circle
i.e. the four circles -> πx2
and the overlayed circle -> π(x+B/2)2

Or there maybe an easier way I have overlooked??

Thank you.

NOTE:
The surface area of the four circles uses the formula πr2, but where r = x/2 and for four identical circles is 4 x π(x/2)2 which is 4πx2/4 which is πx2

Sorry if I'm not very familiar with using the correct symbols on this platform.
 

Attachments

  • Quas-Array-Device-Comparrison.jpg
    Quas-Array-Device-Comparrison.jpg
    52 KB · Views: 778
Last edited:
Mathematics news on Phys.org
  • #2
Make a triangle with the centers of two "S" circles and one "N" circle (or vice versa), and you'll find a method that is much easier than area calculations.
 
  • Like
Likes magnetics
  • #3
Right you are mfb.
Thank you!
 

Related to Calculating area of multiple connected circles

1. How do you determine the total area of multiple connected circles?

The total area of multiple connected circles can be determined by adding the individual areas of each circle. This can be done by using the formula A = πr^2, where A is the area and r is the radius of each circle. Once the individual areas are calculated, they can be added together to get the total area.

2. Can the circles overlap and still be included in the calculation of total area?

Yes, the circles can overlap and still be included in the calculation of total area. In this case, the overlapping area will be counted twice, once for each circle that it belongs to.

3. How do you handle partial circles when calculating area of multiple connected circles?

Partial circles can be handled by determining the fraction of the circle that is being included in the calculation. This can be done by dividing the angle of the partial circle by 360 degrees and then multiplying it by the area formula, A = πr^2, to get the partial area. This partial area can then be added to the total area of the other complete circles.

4. Is there a limit to the number of circles that can be included in the calculation?

No, there is no limit to the number of circles that can be included in the calculation. As long as the circles are connected and their areas can be determined, they can be included in the total area calculation.

5. Can the calculation of area of multiple connected circles be applied to real-life scenarios?

Yes, the calculation of area of multiple connected circles can be applied to real-life scenarios, such as determining the total area of overlapping crops in a field, or calculating the area of overlapping bubbles in a bubble bath. It can also be used in engineering and architecture for determining the total area of overlapping structures.

Similar threads

Replies
1
Views
781
Replies
7
Views
2K
Replies
5
Views
2K
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
1K
Replies
6
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
1K
Replies
2
Views
2K
Back
Top