Sand is being poured into a truck for delivery to a building site.

At time $t$, the sand is being poured in at a rate of

1. Let $V$ be the volume of sand in the truck at time $t.$ Complete the table below:

   $$\begin{array}{ll}t& \frac{dV}{dt}\\ 0& 0\\ 2& 2.4484\\ 4& \\ 6& \\ 8& \\ 10& \\ 12& \end{array}$$

2. Hence, use a Riemann sum to estimate the amount of sand that was poured into the container during the first $12$ seconds.

3. Given that the truck initially contained $120{\text{m}}^3$ of sand, find the amount of sand in the truck after $12$ seconds.

4. Write an expression, using $\int$ notation, which represents the exact amount of sand in the truck after $12$ seconds.

Give your answer to (c), in ${\text{m}}^3$, correct to $3$ significant figures.