Question: Marsha is baking a cake using a pan that is $8$ inches $\times$ $9$ inches $\times$ $11$ inches. She is going to fill the pan $\frac{3}{4}$ of the way full. How many cubic inches of cake batter will be needed?
1. **State the problem:** We need to find the volume of cake batter required to fill a pan that measures $8$ inches by $9$ inches by $11$ inches, but only $\frac{3}{4}$ full.
2. **Formula for volume of a rectangular prism:**
$$\text{Volume} = \text{length} \times \text{width} \times \text{height}$$
3. **Calculate the total volume of the pan:**
$$\text{Volume} = 8 \times 9 \times 11$$
$$= 72 \times 11$$
$$= 792 \text{ cubic inches}$$
4. **Calculate the volume of batter needed:**
Since the pan is filled $\frac{3}{4}$ full, multiply the total volume by $\frac{3}{4}$:
$$\text{Batter volume} = 792 \times \frac{3}{4}$$
Show intermediate step with cancellation:
$$= 792 \times \frac{\cancel{3}}{\cancel{4}}$$
Simplify $792 \times \frac{3}{4}$:
$$= 792 \times 0.75$$
$$= 594 \text{ cubic inches}$$
5. **Answer:** Marsha will need $594$ cubic inches of cake batter to fill the pan $\frac{3}{4}$ full.