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.