Question

Find the volume of the pyramid. Example 1 I need a better explanation for this problem.

Answer 1

Answer:

36 m³

Explanation:

The volume of the pyramid can be calculated as

$V=B\cdot h\cdot\frac{1}{3}$

Where B is the area of the base and h is the height of the pyramid. In this case, the height of the pyramid is 9 m, so, we will need to replace h = 9 m

The base of the pyramid is a triangle, so the area of the base is

$\begin{gathered} B=\frac{1}{2}\cdot base\text{ of triangle}\cdot height\text{ of triangle} \\ \\ B=\frac{1}{2}\cdot4\cdot6 \\ \\ B=\frac{1}{2}\cdot24 \\ \\ B=12 \end{gathered}$

Then, replacing B = 12 and h = 9, we get that the volume of the pyramid is

$\begin{gathered} V=12\cdot9\cdot\frac{1}{3} \\ \\ V=108\cdot\frac{1}{3} \\ \\ V=36 \end{gathered}$

Therefore, the volume is 36 m³