Question

I need to know what numbers to use to find the volume. Can you answer this one as an example, then I can solve the rest.

Answer 1

The volume of a triangular pyramid is given by

$V=\frac{1}{3}\times A\times H$

where H is the heigh of the pyramid and A is the base of the triangular base. In our case,

$H=14mm$

and the base area is

$\begin{gathered} A=\frac{1}{2}base\times\text{height} \\ A=\frac{1}{2}11\times10.6mm \\ A=58.3mm^2 \end{gathered}$

where

Then, by substituting our last result into the volume formula, we have

$\begin{gathered} V=\frac{1}{3}\times A\times H \\ V=\frac{1}{3}\times58.3\times14 \end{gathered}$

which gives

$V=272.0666mm^3$

Therefore, by rounding to the nearest thousandth, the answer is: 272.067 cubic milimeters