Question: A sea lion enclosure has a cuboid-shaped pool with dimensions $4$ m by $13$ m by $6$ m.
A zookeeper decides that there should be at least $20$ m$^3$ of space in the pool for every sea lion living in the enclosure.
Work out the maximum number of sea lions that can live in the enclosure.
1. **State the problem:** We need to find the maximum number of sea lions that can live in a cuboid pool with dimensions $4$ m, $13$ m, and $6$ m, given that each sea lion requires at least $20$ m$^3$ of space.
2. **Calculate the volume of the pool:** The volume $V$ of a cuboid is given by the formula:
$$V = \text{length} \times \text{width} \times \text{height}$$
Substitute the given dimensions:
$$V = 4 \times 13 \times 6$$
3. **Calculate the volume:**
$$V = 52 \times 6 = 312 \text{ m}^3$$
4. **Determine the maximum number of sea lions:**
Each sea lion requires $20$ m$^3$, so the maximum number $N$ is:
$$N = \frac{312}{20}$$
5. **Simplify the fraction:**
$$N = \frac{\cancel{312}}{\cancel{20}} = 15.6$$
6. **Interpret the result:** Since the number of sea lions must be a whole number and each needs at least $20$ m$^3$, the maximum number is the greatest whole number less than or equal to $15.6$, which is $15$.
**Final answer:**
The maximum number of sea lions that can live in the enclosure is **15**.