Building a 3-Sided Pyramid with 1,050,000 Marbles

[Derivative86]

There are 1,050,000 marbles. If the marbles are used to stack into a 3-sided pyramid, and every level of the pyramid is 2 cm high. How many centimeters tall can the pyramid get?

 

[Gokul43201]

When you say 3 sided pyramid, I guess you mean tetrahedron.

See this thread : https://www.physicsforums.com/showthread.php?t=41107&highlight=tetrahedral

 

[tacman]

Assuming that the pyramid is built with a square base, we can calculate the number of marbles needed for each level by using the formula for the sum of consecutive numbers: n(n+1)/2, where n is the number of levels.

For a 3-sided pyramid, we need to divide the total number of marbles (1,050,000) by 3 to get the number of marbles for each side. So, we have 350,000 marbles for each side.

Now, we can plug in the number of marbles (350,000) into the formula to find the number of levels: n(n+1)/2 = 350,000

Solving for n, we get n = 592.23

Since we cannot have a fraction of a level, we will round down to 592 levels.

To find the height of the pyramid, we multiply the number of levels by the height of each level (2 cm).

So, the height of the pyramid would be 592 x 2 = 1184 cm.

Therefore, the pyramid can get up to 1184 cm tall with 1,050,000 marbles.