Question

Find the volume of the triangular pyramid to the nearest whole number.

Answer 1

Check the picture below.

so the base of the pyramid is just a triangle with a base of 19 and an altitude of 13, and the pyramid has a height of 22.

`\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3}~~ \begin{cases} B=\stackrel{base}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=(1)/(2)(19)(13)\\\\ h=22 \end{cases}\implies \begin{array}{llll} V=\cfrac{1}{3}\left[ \cfrac{1}{2}(19)(13) \right](22) \\\\\\ V=\cfrac{2717}{3}\implies V\approx 906~in^3 \end{array}`

Answer 2

Answer: 906 in^3.

Explanation:

The volume of a triangular pyramid is the area of the base multiplied by the height divided by 3.

First, we can start by finding the area of the base.

The area of the base is equal to 19*13/2

= 123.5 in^2

Next, we plug in the formula.

So the volume = 123.5*22/3 in^3

= 905.666 repeated in ^3

Rounded to the nearest whole number is 906 in^3.