1. **State the problem:** We need to find dimensions of a pyramid with a square base that result in a volume of 36 cubic units. 2. **Formula for the volume of a pyramid:** $$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$$ For a square base with side length $s$, the base area is: $$\text{Base Area} = s^2$$ So the volume formula becomes: $$V = \frac{1}{3} s^2 h$$ where $h$ is the height of the pyramid. 3. **Given:** $$V = 36$$ 4. **Find dimensions:** We want to find $s$ and $h$ such that: $$36 = \frac{1}{3} s^2 h$$ Multiply both sides by 3: $$108 = s^2 h$$ 5. **Choose a value for $s$ and solve for $h$:** Let's pick $s = 6$ units. Then: $$108 = 6^2 \times h = 36h$$ Divide both sides by 36: $$\cancel{36}h = \frac{108}{\cancel{36}}$$ $$h = 3$$ 6. **Check the volume:** $$V = \frac{1}{3} \times 6^2 \times 3 = \frac{1}{3} \times 36 \times 3 = 36$$ **Answer:** A pyramid with a square base of side length 6 units and height 3 units has a volume of 36 cubic units.