Question on volume of swimming pool

Question

Swimming pool is of length 20m, wide 5m and height of the swimming pool increase from the 1.6m to 4.4m.

What is the volume of swimming pool?

How I approached: Area of swimming pool = Area of cube + Area of prism

Area of cube = l * b * h

So

Area of cube = 20 * 5 * 1.6 Are of prism = ???

Answer 1

No calc needed here:

$20\times5\times1.6$ for the cube $= 160$.

$20 \times 5 \times \frac{ 4.4 - 1.6 }2$ for the prism $= 140$ (just take the average of the two heights since the bottom is flat, if it were curved then we get into calc).

Total is $300$.

Answer 2

Assuming the height $h$ increases linearly with respect to its length $l$, i.e. height $h=1.6+2.8 (l/20)$ the volume corresponding to the infinitesimal region with height $h$ is $ 5 h dl$. Thus total volume is $$\int_{0}^{20} 5 hdl=\int_{0}^{20} 5( 1.6+2.8 (l/20) )dl=160+140=300.$$