Estimate how many books can be shelved in a college library with 3500 square meters of floor space. Assume 8 shelves high on both sides, with corridors 1.5 wide. The books are about 4 cm thick on average.

The answer is 700,000 books but I don't know how to get it.

Hello emat22

Ok : 3500 square meters of floor space.
That is 50 x 70 meters of floor space.
Per corridor you require double book/shelf width (one book/shelf width=approx 250mm) + 1,5m walkspace, i.e around 2 meter.
That allows 50/2 = 25 corridors.
Each corridor allows for 2 raws of books, i.e. 2 x 25 x 70 = 3500 meters of book space.
That amount goes times 8 (shelves per meter), i.e. 3500 x 8 = 28.000 meters of book space.
Per meter there are 100/4 = 25 books. Total book capacity is therefore 25 x 28.000 = 700.000 meters of book space.

Well, that was not too difficult, was it not??

:>)

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Thank you so much!

Quote:

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Originally Posted by Unknown008

Don't quite understand but good job here, Cred!

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Thanks Unknown008 !

If you don't "get" that, I should explain it better, so here I go again :

Number of books depends on the total meters of available shelf space.
3500 sq. meters of floor space means 50 x 70 m. (100 x 35 m. works just as well).
Walking space is 1,5 m. per corridor. Add approx. book shelf width at both sides = 2 x 250 mm = 0,5 m. Total corridor space becomes 1,5 m + 0,5 m = 2 m.
On 50 m. that allows 50/2 = 25 corridors (of 70 m. each).
Total corridor length = 25 x 70 = 1750 m. with 2 shelf spaces.
There are 8 shelves on top of each other = 8 x 2 x 1750 m = 28.000 m. of shelf length.
With books of 4 cm thick, there are 100/4 = 25 books per m.
Max. number of books = 25 x 28.000 = 700.000 books.

Capice?

:>)

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Capice!;)

How did you get 100, when you divided it by 4?

How did he get 100 when he divided it by 4?

I know this question has been answered, but the person used periods where commas should have been used and used commas where periods should have been. This caused me a lot of confusion and I ended up just doing the problem myself. Now remember, this is an Estimation... Your answer in the end should be a rounded number!

Assuming you are using my Physics book.. It is .04m thick and has a width of .22m. Since the shelves will be double sided you will need at least .46m thick shelves after adding a .02m thick separation. Rounded, the shelves are .50m.

Since the room is 3,500m^2 it is approximately 60m by 60m. Now... for the math...

60m (width of room) / 2m (space required plus shelf width) = 30 rows of shelves.
30 rows of shelves * 8 (height of shelves) = 240 shelves per side.
240 shelves per side * 2 (for each side) = 480 shelves total. (Remember number)

60m (length of rows/shelves) / .04m (thickness of books) = 1,500 books per shelf.
480 shelves * 1,500 books per shelf = 720,000 books total.

720,000 approximately equals 700,000!

Your answer should be 7 * 10^5