My daughter received a game that required lots of maths puzzles to be solved. She has solved most of them but this one has her and all the rest of us stumped. There is obviously some formula for working it out but I don't know what it is and despite days of trying have had no luck can anyone here help?

This is the problem, A stained glass window has 9 symmetrical panes with a design in each - a quarter circle in each corner and a central circle in the gap left. Each pane is 4in (101.6mm) square. The lead boundary strip overlaying each separate piece of glass is an eighth of an inch (3.17mm) thick and where they meet they merge to 3.17mm (no double thicknesses), what area of glass is needed for the small sections of the central circles? (Assume that pi = 3.14) I would be grateful for any pointers.

regards
Lynette

Lynette, the radius of each quarter-circle of glass is $(4-1/8)/2$ inches $=31/16$. The area of each 1/4 circle is $(1/4)\pi \times r^2$. So the area of the 36 quarter circles is

$36\times (1/4)\times \pi \times (31/16{)}^2$

For the central circles, look at the diagonal of each window pane. The outside diameter of the lead boundary of the quarter pane is the distance of the inside glass circle from one corner:

(33/16) inches

The total distance from corner to corner is

$4\times \sqrt{2}$ inches.

So the diameter of the inner circle is

$4\times \sqrt{2}-(33/16)-(33/16)$ inches.

The radius of the inner circle of glass is

$2\times \sqrt{2}-(33/16)$ inches.

There are 9 of these, so their area is

$9\times \pi \times (2\times \sqrt{2}-(33/16{))}^2$ inches.

Is that it? 36 quarter circles and 9 smaller full circles?

If so, add up the areas, and you get the total area of the glass.

If there are more little pieces of glass whose area you need to find, upload the picture, and I'm sure someone (maybe me, if I get to it first) will help you.

Graeme, thank you very much for the reply. I managed to get it with your help. The answer was 16.58 sq in. Certainly has made me use my old brain, I'd forgotten how interesting maths could be!

regards
Lynette

The Pharaoh's cook is extremely fussy about how his kitchen looks. He has a big, square box of 81 eggs (9 rows with 9 eggs in each row). He's about to make an enourmous 48 egg omelette for the Pharaoh's family, but can't bear to leave an unsymmetrical pattern of eggs in the box. In fact he's so fussy, that he wants the pattern to be symmetrical when viewed from any corner or any side, and wants there to be 16 rows of eggs, with five eggs in each row! Can you make such a pattern with the remaining 33 eggs?

Just mark the eggs with an E if possible

EG.


E E E E E E E E E
E
E
E
E
E


Hope this makes sense!!

Regards,
Lynette's daughter Stephanie
xx

Well I don't know if you'll like this, but it does have 16 rows of five eggs each. It has other rows of 6, rows of 2, and rows with other numbers of eggs as well. And it is symmetrical. See what you think...

YES!! Thankyou SOOO much i have completed the whole thing now and i couldnt of done it without your help!!

Sorry it took so long to reply but my server has been down for the last week and i havent had the chance to get on the internet!!

But thankyou so much for all the replys and especially graeme coz u worked it out!!!

Regards
Lynettes daughter Stephanie