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To solve this problem, we need to use the formula for the volume of a square pyramid:

\[
V = \frac{1}{3} \times b^2 \times h
\]

where:
- \(V\) is the volume,
- \(b\) is the length of a side of the square base,
- \(h\) is the height of the pyramid.

We are given:
- \(V = 75 \, \text{cm}^3\),
- \(h = 9 \, \text{cm}\).

We need to find \(b\), the side length of the base. Substituting the known values into the formula:

\[
75 = \frac{1}{3} \times b^2 \times 9
\]

Simplifying:

\[
75 = 3b^2
\]

Now, solve for \(b^2\):

\[
b^2 = \frac{75}{3} = 25
\]

Finally, take the square root of both sides to find \(b\):

\[
b = \sqrt{25} = 5 \, \text{cm}
\]

So, the correct answer is **5 cm**.

Would you like any more details or further explanations?

Here are 5 related questions:
1. How do you find the volume of different types of pyramids?
2. How does changing the height affect the volume of a pyramid?
3. What is the formula for the surface area of a square pyramid?
4. How can the Pythagorean theorem be applied in a pyramid?
5. What is the difference between the volume of a cone and a pyramid?

**Tip:** For any solid figure with a uniform cross-section (like a pyramid or cone), the volume can be found using a fraction of the area of the base multiplied by the height.

A square pyramid has a height of 9 cm and a volume of 75 cm³. What is the length of a side of the base?

Learn how to calculate the length of a square pyramid's base given its height (9 cm) and volume (75 cm³). This solution involves applying the formula for the volume of a square pyramid and solving for the base side length. Suitable for students in Grades 7-9.

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