Question

What's the volume?


I honestly just need the formula.

Answer 1

`v=364.5\ m^3`

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

`\displaystyle A_t=(b_1+b_2)/(2)h`

where
`b_1` and
`b_2` 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

`\displaystyle v=A_t\ x`

`\displaystyle v=(b_1+b_2)/(2)\ h\ x`

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:

`\displaystyle b_1=7m,\ b_2=11m,\ h=4.5m,\ x=9m`

We now compute the volume

`\displaystyle v=(7+11)/(2).(4.5)(9)=364.5`

`\boxed{\displaystyle v=364.5\ m^3}`