Question: A truck is used to transport some wood panels.
Each wood panel is a cuboid measuring $2.4$ m by $1.2$ m by $1.8$ cm.
The density of each wood panel is $750$ kg/m$^3$.
The truck can carry $15$ tonnes of these wood panels.
Calculate the maximum number of wood panels that the truck can carry.
1. **State the problem:** We need to find the maximum number of wood panels the truck can carry given the dimensions and density of each panel and the truck's carrying capacity.
2. **Convert all units to meters:** The thickness is given as $1.8$ cm, which is $\frac{1.8}{100} = 0.018$ m.
3. **Calculate the volume of one wood panel:**
$$\text{Volume} = 2.4 \times 1.2 \times 0.018 = 0.05184 \text{ m}^3$$
4. **Calculate the mass of one wood panel using density:**
$$\text{Mass} = \text{Density} \times \text{Volume} = 750 \times 0.05184 = 38.88 \text{ kg}$$
5. **Convert truck capacity to kg:**
$$15 \text{ tonnes} = 15 \times 1000 = 15000 \text{ kg}$$
6. **Calculate the maximum number of panels:**
$$\text{Number of panels} = \frac{15000}{38.88}$$
7. **Simplify the fraction showing cancellation:**
$$\frac{15000}{38.88} = \frac{\cancel{15000}}{\cancel{38.88}} \approx 385.8$$
8. Since the number of panels must be whole, the truck can carry a maximum of **385** wood panels.
**Final answer:** The truck can carry a maximum of **385** wood panels.