Question: What is the volume of the following rectangular prism?
$3 \frac{1}{3}$ units$^2$
$1 \frac{2}{5}$ units
Volume = _____ units$^3$
1. **State the problem:** We need to find the volume of a rectangular prism given the area of its base and its height.
2. **Given:**
- Base area $A = 3 \frac{1}{3}$ units$^2$
- Height $h = 1 \frac{2}{5}$ units
3. **Formula:**
The volume $V$ of a rectangular prism is given by:
$$V = A \times h$$
4. **Convert mixed numbers to improper fractions:**
- $3 \frac{1}{3} = \frac{10}{3}$
- $1 \frac{2}{5} = \frac{7}{5}$
5. **Calculate the volume:**
$$V = \frac{10}{3} \times \frac{7}{5}$$
6. **Multiply the fractions:**
$$V = \frac{10 \times 7}{3 \times 5} = \frac{70}{15}$$
7. **Simplify the fraction:**
$$V = \frac{\cancel{70}^{14}}{\cancel{15}^{3}} = \frac{14}{3}$$
8. **Convert back to mixed number:**
$$\frac{14}{3} = 4 \frac{2}{3}$$
9. **Final answer:**
The volume of the rectangular prism is $4 \frac{2}{3}$ units$^3$.