The Solution:
Given:
We are asked to find the volume.
Observe that the base surface that can give a uniform cross-section is a trapezoid.
So, the formula for the volume is:
[tex]Volume=\frac{1}{2}(a+b)h\times H[/tex]
In this case:
[tex]\begin{gathered} a=1m \\ \\ b=4m \\ \\ h=height\text{ of the trapezoid}=? \\ \\ H=10m \end{gathered}[/tex]
Find h:
[tex]\begin{gathered} h^2+3^2=30^2 \\ \\ h^2=900-9 \\ \\ h^2=891 \\ \\ h=\sqrt{891}=29.8496m \end{gathered}[/tex]
Substitute:
[tex]Volume=\frac{1}{2}(1+4)29.85\times10=5\times29.85\times5=746.241m^3[/tex]
Therefore, the correct answer is 746.241 cubic meters.
