Question

A hole must be excavated for a swimming pool in the shape shown in the figure. Whatvolume of depth must be removed in order to create this hole?10 m30 m1 m4 m

Answer 1

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:

`Volume=(1)/(2)(a+b)h* H`

In this case:

`\begin{gathered} a=1m \\ \\ b=4m \\ \\ h=height\text{ of the trapezoid}=? \\ \\ H=10m \end{gathered}`

Find h:

`\begin{gathered} h^2+3^2=30^2 \\ \\ h^2=900-9 \\ \\ h^2=891 \\ \\ h=√(891)=29.8496m \end{gathered}`

Substitute:

`Volume=(1)/(2)(1+4)29.85*10=5*29.85*5=746.241m^3`

Therefore, the correct answer is 746.241 cubic meters.