Question

Find the volume. Round if necessary. 4 km 5 km 12 km 2 km Doc 8 km

Answer 1

The volume is 16.36 cubic kilometers

Explanation:

We have the formula to calculate the volume of the figure would be:

`V=A_b\cdot h`

The height is known to be 2 km, we must calculate the area of the base, which is a triangle and we can calculate it as follows:

`\begin{gathered} A_b=\sqrt[]{s\cdot(s-a)\cdot(s-b)\cdot(s-c)} \\ \text{where s is the semiperimeter } \\ s=(p)/(2) \\ p=4+5+8 \\ p=17 \\ \text{replacing} \\ s=(17)/(2)=8.5 \\ \text{ now, replacing in the area} \\ A_b=√(8.5\cdot\left(8.5-4\right)\cdot\left(8.5-5\right)\cdot\left(8.5-8\right)) \\ A_b=8.18 \end{gathered}`

Now, replacing in the volume:

`\begin{gathered} V=\text{8}.18\cdot2 \\ V=16.36 \end{gathered}`