How many 1 inch diameter circles can fit in a 9 inch diameter circle?

Question

How many 1 inch diameter circles can fit in a 9 inch diameter circle?

Answer 1

This Site Might Help You.



RE:

How many 1 inch diameter circles can fit in a 9 inch diameter circle?

How many 1 inch diameter circles can fit in a 9 inch diameter circle?

Answer 2

Calculate the volume of the 9 inch circle, subtract 30% for wasted space, then divide by the volume of the 1 inch circle.

Answer 3

See, there can be 2 types of answer to these type of questions.

1. You want to know how many circles of 1" diameter you can CUT OUT from a circle of 9" diameter (considering wastage of area)

OR

2. You want to know how many circles of 1" diameter can FIT IN ANYHOW within a circle of 9" diameter (here you do not consider wastage of area).

---------------------------------------------------------------------------------------------------

FIRST OPTION:

In this case, you have to consider how many SQUARES of side 1" (equal to the diameter of small cirlces) can be cut out (or fitted into) a circle of 9" diameter.

You consider a square, because if you draw few circles side by side, you'll see that there are some small spaces in between 2 adjacent circles. These small spaces are wastage of area, and do not contribute to making another circle.



So your number of cirlces =

[area of bigger circle (of 9/2" radius)] ÷ [area of square with side equal to diameter of smaller cirlces (1" here)]

= (π × 4.5" × 4.5") ÷ (1" × 1")

= 63.585 (taking π = 3.14)

If the answer is a fraction, then take the WHOLE NUMBER PART OF THE FRACTION, as you want only complete circles.



So, the answer is --> 63 circles

------------------------------------------------------------------------------------------------------

However if you do not want to consider wastage of paper (though it is rarely done so), then you simply divide the area of the bigger circle by the area of the smaller circle.

(But I don't think this is correct, as you can't always create a perfect circle from the wasted bits of paper).



The anser in that case would be (π × 4.5 × 4.5) ÷ (π × 0.5 × 0.5)

= 81 circles

Answer 4

One will sure fit in! Oh! Did you mean maximum number of circles?

Answer 5

The best packing is so that the centres of the circles form equilateral triangles.

To pack them like this, and facilitate counting at the same time, place 1" circles so that they form 3 evenly spaced diagonals, and form 6 segments. This takes 6 * 4 + 1 = 25 circles.

Now fill in the 6 segments with 6 each - that is all that will fit.

So, 25 + 36 = 61.



6 * 10 + 1 ???

Does that suggest another fill/count method?



An odd multiple for the diameter of the large circle will give a one-in-the-centre filling pattern. An even multiple will give a different filling pattern.

Answer 6

if dis is not practical & jus a book question den ::

d ans is 81

Answer 7

interesting question. i suggest you must draw it to find the answer because calculating such thing can be difficult. but maybe some of the other answerers got some idea how to calculate this problem.



remember: the answer is not AREA FOR A 9 INCH DIAMETER CIRCLE divided over AREA FOR A 1 INCH DIAMETER CIRCLE

Answer 8

Put a penny on the table.



Surround the penny with a ring of 6 pennies. The center penny touches each of the other six. This is the most compact shape.



Add another layer of pennies along the outside. The most you can add is 12, in a hexagon.



Add more layers of pennies. Note that with the fourth layer, all the "corner" pennies touch the circle, just like inscribing a hexagon into the circle. You can't add any more layers.



Count the pennies, layer by layer.

center: 1

layer 1: 6

layer 2: 12

layer 3: 18

layer 4: 24

Total: 61



The number of 1-inch circles that can fit inside a 9-inch circle is 61.



http://www.flickr.com/photos/dwread/2766310967/