Question: The driveway also has the depth of $200\text{mm}$
$2000\text{mm}$
$3000\text{mm}$
$4000\text{mm}$
$200\text{mm}$
12. You have been asked to work out the volume of the driveway
to arrange a concrete order. Use the surface area of the top of
the driveway that you calculated in question 1 to now calculate
the volume of concrete required for the $200\text{mm}$ deep slab.
Provide your answer in $m^3$ and write down your formula you
used. *
Show your workings (what did you enter into
your calculator)
Answer (including unit of
measure)
Enter answer here...
Enter answer here...
1. **State the problem:** Calculate the volume of concrete needed for a driveway slab that is $200\text{mm}$ deep, using the surface area of the top of the driveway.
2. **Given dimensions:**
- Short top edge length = $2000\text{mm}$
- Top surface width = $3000\text{mm}$
- Bottom length = $4000\text{mm}$
- Depth (thickness) = $200\text{mm}$
3. **Convert all measurements to meters** (since volume is required in cubic meters):
- $2000\text{mm} = \frac{2000}{1000} = 2\text{m}$
- $3000\text{mm} = \frac{3000}{1000} = 3\text{m}$
- $4000\text{mm} = \frac{4000}{1000} = 4\text{m}$
- $200\text{mm} = \frac{200}{1000} = 0.2\text{m}$
4. **Calculate the surface area of the top of the driveway:**
Since the driveway is wedge-shaped, the top surface is a trapezium with parallel sides $2\text{m}$ and $4\text{m}$ and width $3\text{m}$.
Formula for area of trapezium:
$$\text{Area} = \frac{(a + b)}{2} \times h$$
where $a = 2\text{m}$, $b = 4\text{m}$, and $h = 3\text{m}$.
Calculate:
$$\text{Area} = \frac{(2 + 4)}{2} \times 3 = \frac{6}{2} \times 3 = 3 \times 3 = 9\text{ m}^2$$
5. **Calculate the volume of concrete:**
Volume = Surface area $\times$ Depth
$$\text{Volume} = 9 \text{ m}^2 \times 0.2 \text{ m} = 1.8 \text{ m}^3$$
6. **Final answer:**
The volume of concrete required is **$1.8\text{ m}^3$**.
7. **Summary formula used:**
$$\text{Volume} = \text{Surface Area} \times \text{Depth}$$
8. **Calculator input example:**
- Calculate area: $(2 + 4) / 2 \times 3 = 9$
- Calculate volume: $9 \times 0.2 = 1.8$