Answer:
[tex]v=364.5\ m^3[/tex]
Step-by-step explanation:
Volume Of A Regular Solid
When a solid has a constant cross-section, the volume can be found by multiplying the area of the base by the height. The area of a trapezium is
[tex]\displaystyle A_t=\frac{b_1+b_2}{2}h[/tex]
where [tex]b_1[/tex] and [tex]b_2[/tex] are the lengths of the parallel sides and h the distance between them.
The figure shows a solid with a trapezoid as the constant cross-section and a height x. The volume of the solid is
[tex]\displaystyle v=A_t\ x[/tex]
[tex]\displaystyle v=\frac{b_1+b_2}{2}\ h\ x[/tex]
The image doesn't explicitly say if the length of 4.5 is the height of the trapezium or the length of that side. We'll assume the first, so our data is:
[tex]\displaystyle b_1=7m,\ b_2=11m,\ h=4.5m,\ x=9m[/tex]
We now compute the volume
[tex]\displaystyle v=\frac{7+11}{2}.(4.5)(9)=364.5[/tex]
[tex]\boxed{\displaystyle v=364.5\ m^3}[/tex]
