Annulus

Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n.

Result

n =  4

Solution:

r1=1 r2=9  r=(r2r1)/2=(91)/2=4  R=r1+r=1+4=5  a=r=4  o1=2π R=2 3.1416 531.4159  n1=o1/(2 r)=31.4159/(2 4)3.927   n=4  θ=180/n=180/4=45  ρ=r1 sin(θ)1sin(θ)=1 sin(45)1sin(45)2.4142 R2=r+2 ρ=4+2 2.41428.8284 R2<Rr_{1}=1 \ \\ r_{2}=9 \ \\ \ \\ r=(r_{2}-r_{1})/2=(9-1)/2=4 \ \\ \ \\ R=r_{1}+r=1+4=5 \ \\ \ \\ a=r=4 \ \\ \ \\ o_{1}=2 \pi \cdot \ R=2 \cdot \ 3.1416 \cdot \ 5 \doteq 31.4159 \ \\ \ \\ n_{1}=o_{1}/(2 \cdot \ r)=31.4159/(2 \cdot \ 4) \doteq 3.927 \ \\ \ \\ \ \\ n=4 \ \\ \ \\ θ=180/n=180/4=45 \ ^\circ \ \\ ρ=\dfrac{ r_{1} \cdot \ \sin(θ) }{ 1-\sin(θ) }=\dfrac{ 1 \cdot \ \sin(45^\circ ) }{ 1-\sin(45^\circ ) } \doteq 2.4142 \ \\ R_{2}=r + 2 \cdot \ ρ=4 + 2 \cdot \ 2.4142 \doteq 8.8284 \ \\ R_{2}<R



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
See also our trigonometric triangle calculator.

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Circles
    three-circles Three circles of radius 95 cm 78 cm and 64 cm is mutually tangent. What is the perimeter of the triangle whose vertices are centers of the circles?
  2. Candies
    bonbons_2 In the box are 12 candies that look the same. Three of them are filled with nougat, five by nuts, four by cream. At least how many candies must Ivan choose to satisfy itself that the selection of two with the same filling? ?
  3. Guppies for sale
    guppies Paul had a bowl of guppies for sale. Four customers were milling around the store. 1. Rod told paul - I'll take half the guppies in the bowl, plus had a guppy. 2. Heather said - I'll take half of what you have, plus half a guppy. The third customer, Na
  4. Five-gon
    5gon_diagonal Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.
  5. Construct
    inscircle_triangle Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction and description.
  6. Chords
    chords How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones?
  7. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  8. Candy - MO
    cukriky_4 Gretel deploys to the vertex of a regular octagon different numbers from one to eight candy. Peter can then choose which three piles of candy give Gretel others retain. The only requirement is that the three piles lie at the vertices of an isosceles triang
  9. Centre of mass
    centre_g_triangle The vertices of triangle ABC are from the line p distances 3 cm, 4 cm and 8 cm. Calculate distance from the center of gravity of the triangle to line p.
  10. Average
    chart If the average(arithmetic mean) of three numbers x,y,z is 50. What is the average of there numbers (3x +10), (3y +10), (3z+10) ?
  11. Trigonometry
    sinus Is true equality? ?
  12. Cards
    cards_2 Suppose that are three cards in the hats. One is red on both sides, one of which is black on both sides, and a third one side red and the second black. We are pulled out of a hat randomly one card and we see that one side of it is red. What is the probab
  13. Legs
    rak Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects?
  14. Teams
    football_team How many ways can divide 16 players into two teams of 8 member?
  15. Sequence 2
    seq2 Write the first 5 members of an arithmetic sequence a11=-14, d=-1
  16. AP - simple
    sigma_1 Determine the first nine elements of sequence if a10 = -1 and d = 4
  17. Blocks
    cubes3_1 There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?