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The question in the image is about finding the total number of layers in a pyramid made from steel balls, given that the number of balls in each layer follows a specific pattern.

**Information provided:**
- There are 8436 steel balls, each with a diameter of 1 cm.
- The balls are arranged in a pyramid.
- The pattern of balls per layer is:
  - 1 ball in the first layer,
  - 3 balls in the second layer,
  - 6 balls in the third layer,
  - 10 balls in the fourth layer,
  - and so on.

This is a pattern of triangular numbers. The number of balls in the nth layer is given by the formula for the nth triangular number:
\[
T_n = \frac{n(n+1)}{2}
\]
The total number of balls in the pyramid is the sum of the triangular numbers up to a certain number of layers. We need to find how many layers (n) are required to reach or exceed 8436 balls.

### Steps to solve:
1. Sum the triangular numbers \( T_1, T_2, T_3, \dots \) until the sum equals or exceeds 8436.
2. Find the number of layers (n) corresponding to that sum.

Let me calculate this for you.The total number of layers required to use exactly 8436 steel balls is 36.

Thus, the correct answer is **C) 36**.

Would you like more details or explanations on how this was calculated?

Here are 5 related questions:
1. How do triangular numbers work in mathematical sequences?
2. Can the triangular number formula be applied to other geometric arrangements?
3. What is the significance of the sum of triangular numbers in real-life structures?
4. How can the sum of other polygonal numbers (e.g., square numbers) be calculated?
5. How would the calculation change if the balls' sizes were different?

**Tip:** In sequences like this, recognizing patterns early on helps simplify solving the total.

8436 स्टील की गेंदें हैं, जिनमें से प्रत्येक की त्रिज्या 1 cm है। इन्हें एक ढेर में इस प्रकार रखा गया है कि शीर्ष पर 1 गेंद, दूसरी परत में 3 गेंदें, तीसरी परत में 6 गेंदें, चौथी परत में 10 गेंदें हैं। इस प्रकार अन्य परतों में गेंदों की संख्या की गणना करें।

Learn how to calculate the number of layers required to stack 8436 steel balls arranged in a pyramid following a triangular number pattern. Suitable for Grades 8-10, this problem involves arithmetic sequences, summation, and triangular numbers.

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