In 8,192 square feet, how many blocks will fit?

Question

Ok... it's a square of 8,192 square feet and each block is 8 inches in height and 16 inches in length. How many of these blocks can fit in that amount of square feet?!? Seem simple?!? Think again...

Help please!!!

Answer 1

I think that you can fit only 9112 blocks because your box is square. I arrived at this number because I found the side lengths of the box which is 1086 inches (90.5 feet).

Since the bricks are shaped like this:
----------
|............|8
16

I layed the bricks down that way all the way up the wall. Since that means only 8 inches are touching the wall, you can fit 135. Then going across the bottom you can fit 67 because it is going the long way, taking up 16 inches each. But you have enough room to stand a brick upright at the other wall, because you have about 10 inches left.

This means you can fit 135x67 bricks laying flat, and another 67 standing up (since they take up 16 inches on that wall, and there is only room for one column of them).

So through basic math I arrived at the answer of 9112 bricks.

Ideally, however you could fit 9216 bricks, but that would call for a specified size of each wall of the box.

Answer 2

My science teacher pulled a similar question. Anyway...

8 inches is 2/3 of a foot
16 inches is 4/3 of a foot

multiply these together to get 8/9 of a square foot.
How many 8/9's fit into 8,192?

Divide 8,192 by 8/9 and you get.... 9,216 blocks.

PS to the first answerer... I really do not understand how 8x16 equals 24 inches square. 8x16 multiplied out is 128 square inches. And a square foot is 12 inches by 12 inches which is 144 square inches, not 24. It is multiplying, not adding.

It wouldn't exactly fit, but in theory it is right around 9,216 give or take a 0.0000000000000001 or so. :)

Answer 3

Since you specify only the area and not the precise dimensions of the space, we have to assume a general case. Thus we look only at the area of the space and the area of an individual block.
Area of a block in square feet
8*16/144 = 0.8888... square feet = 8/9 square feet

Area of the floor
8192 s.f.

Number of blocks:
8192/0.888888... = 8192*9/8 = 9,216 blocks

Answer 4

If I convert to square inches.

8,192 x 144 = 1179648

The block is 16 x 8 = 128

So 1179648 / 128 = 9216

So 9216 blocks (theoretical)

Practical is different if they must be whole and it must be a square.

90.51 on each side or 1086 inches

The easy answer is <<9045>> but you may be able to mix them to get another row in.

One side must be 135 x67 whole, leaving a 12 inch gap of a different orientation that can fit one row of 67.

Final Answer **********************(9112)**************

Answer 5

2 tiles make a square 1.25 feet on a side
8,192 sq.ft. in a square is sqrt(8 192) = 90.509668 feet on a side. which is 90 feet and 6.116016 inches
It can't be done.

Answer 6

8,192 1 footed blocks