1. **State the problem:** Miguel's aquarium measures 70 cm by 50 cm by 30 cm. It is filled three quarters full of water. We need to find how many liters of water it contains. 2. **Formula for volume of a rectangular prism:** $$V = L \times W \times H$$ where $L$ is length, $W$ is width, and $H$ is height. 3. **Calculate the total volume of the aquarium:** $$V = 70 \times 50 \times 30 = 105000 \text{ cm}^3$$ 4. **Calculate the volume of water when filled three quarters full:** $$V_{water} = \frac{3}{4} \times 105000 = 78750 \text{ cm}^3$$ 5. **Convert cubic centimeters to liters:** Since $1$ liter = $1000$ cm$^3$, $$\text{Liters} = \frac{78750}{1000} = 78.75 \text{ liters}$$ **Final answer:** The aquarium contains **78.75 liters** of water when filled three quarters full.