MAths Homework Help

Flemingovia

Flemingovia

TNPer
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Actually, it is religious education, but the question is maths:

It is for my 13 year old son, and the maths in creating a holocaust memorial is beyond us.

We want to create a pyramid of seven million spherical stones.

Assuming the top layer has one stone, supported on four stones which in turn is supported on nine stones, and so on....

1. How many layers would we need to get seven million stones in total?
2. How many stones would be in the bottom level? (in terms of X by X)?

Thanks.
 
The top layer has 1^2 (= 1) stone, the second layer has 2^2 (= 4) stones, the third has 3^2 (= 9) stones, the fourth has 4^2 (= 16) stones, the nth layer has n^2 stones, etc. You simply need to keep adding layers until you get to eleven million. Hence you need to add squares of each integer until you hit eleven million. This would be extremely tedious but there's a formula for summing squares:

1^2 + 2^2 + 3^2 + ... + n^2 = n(n+1)(2n+1)/6

so for example 1^2 + 2^2 + 3^2 = 3(3+1)(2*3+1)/6 = 3*4*7/6 = 14

Hence, you need to solve the equation n(n+1)(2n+1)/6 = 11,000,000. The solution for n will give you the number of necessary layers, and the number of stones in that layer would be n^2.

Let me know if you have any questions :D
 
Hahaha. ^2 means squared, ^3 is cubed, etc. So 5^2 is five squared which is 5*5 which is 25.

The answer is 320 layers which will give you 10,973,920 spheres (11 million spheres exactly is mathematically impossible; this is as close as we can get). Thus there are 320^2 = 102,400 spheres in the bottom layer.
 
To be honest I'm surprised they're asking him to do this. It is not an easy problem. Either this is an anomaly or the American education system truly is terrible in comparison.
 
John Ashcroft Land:
To be honest I'm surprised they're asking him to do this. It is not an easy problem. Either this is an anomaly or the American education system truly is terrible in comparison.
Click to expand...
Depends on the state in the US, as I've got similar problems like this before at that child's age :ADN:
 
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