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**smartguy_ppl****Member**- Registered: 2005-09-02
- Posts: 3

The base of the pyramid is 100 blocks by 100 blocks; each successive layer is one less block wide and deep, until the top layer which is simply one block. Each block is 97 cm wide by 97 cm deep by 63 cm tall.

If one liter of paint can coat exactly three square meters, how many liters are required to coat the entire exposed surface of the pyramid? Round up to the nearest liter.

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**nvidura****Member**- Registered: 2005-09-01
- Posts: 1

To do this you need to know the visible area in that pyramid since paint can apply only to outer surfers

Use

= (n/2) (n + 1)

= (100/2) (101)

= 5050

This is the number of faces in one surface

since there are 4 surfaces + 1 top surface

= 5050 * 4

= 20 200

The total side area covered by one block is 97* 63

= (97* 63) * 20200

= 123442200cm^2

= 12344.22 m^2

The area of the opened tops

= (100* 100) (97* 97)

= 94090000 cm^2

= 9409 m^2

Total area

= 9409 m^2 + 12344.22 m^2

= 21753.22 m^2

Since paint can apply to 3 sqm

= (21753.22 m^2)/3

= 7251.07 liters

*Last edited by nvidura (2005-09-02 00:50:17)*

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**smartguy_ppl****Member**- Registered: 2005-09-02
- Posts: 3

Are you positive this is right?

BTW, I was wondering why you calcualtated the opened top differetly than the sides. Can you please explain that?

*Last edited by smartguy_ppl (2005-09-02 01:06:38)*

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

I get the same result as nvidura. There are five views: top view (easy), south, west, north, and east views (harder).

So to calculate the south view vertical number of blocks:

You combine the bottom row with the top row making 101 blocks. Then you combine the 2nd row with 2nd row from the top, this also is 101 blocks (99 + 2). So I drew a small one that started out with three, but it was odd, and it wasn't analogous to 100 on the bottom. Then I redrew four on bottom and realized the number of pairs of 101 would be 50. So that's how it goes.

To compute the top surface area:

If you walk up the pyramid, each step is half a block forward from the next; they overlap. But you don't need to worry about

that if you just look at the whole pyramid from an airplane, and just compute the area of the overall square.

Units:

and you can use 0.63 meters and 0.97 meters right off the bat to make things a little easier.

*Last edited by John E. Franklin (2005-09-02 03:22:02)*

**igloo** **myrtilles** **fourmis**

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,626

BTW, paint normally covers 12-16 m² per litre, but you might need 3 coats.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**Sivathanushan Easwaran****Guest**

You guys are all wrong, the answer is 7252 liters

**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

*Sivathanushan Easwaran * is absolutely right!!!

If one liter of paint can coat exactly three square meters, how many liters are required to coat the entire exposed surface of the pyramid?

Round up to the nearest liter.

Forgetting to round answers....could mean the difference between A and A+

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**Sivathanushan Easwaran****Guest**

How about this question?

Suppose you have, say, a stone tablet of some sort. The tablet has 16 pieces missing. But lucky you, you have the pieces! You can tell by looking at the pieces which ones are the four corners, which ones are the eight side pieces, and which ones are the inside pieces. Otherwise, you can't tell where on the tablet they should go or how they should be oriented.

If it takes 90 seconds to place all of the pieces, how many days will it take to try every possible combination? Please round to the nearest full day.

Is the answer 24192 days or 6193152 days.

**Sivathanushan Easwaran****Guest**

any one

**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

I think I have already saw that question somewhere.

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

here is it

http://www.mathsisfun.com/forum/viewtopic.php?id=1598

*Last edited by kylekatarn (2005-09-17 12:47:18)*

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