Question

Find the volume of a pyramid with a square base, where the perimeter of the base is4.1 m and the height of the pyramid is 3.6 m. Round your answer to the nearesttenth of a cubic meter.

Answer 1

The volume of a pyramid is given by the following equation:

$V=\frac{1}{3}A_{\text{base}}\cdot H$

Knowing that the base of this pyramid is a square, the volume will be:

$V=\frac{1}{3}L^2\cdot h$

Recalling that for a square, the area is the square of the length of the sides (L).

We know the perimeter but not the sides, however, for a square, the perimeter is 4 times the lenght of any side, since all sides are equal in length. We can calculate L now:

$\begin{gathered} P=4L \\ L=\frac{P}{4} \\ L=\frac{4.1m}{4} \\ L=1.025m \end{gathered}$

Now, knoing the sides of the base (L=1.025m) and the height of the pyramid (h=3.6m), we can replace values in the equation of the volume:

$\begin{gathered} V=\frac{1}{3}L^2\cdot h \\ V=\frac{1}{3}(1.025m)^2\cdot3.6m \\ V\approx1.26m^3 \\ V\approx1.3m^3 \end{gathered}$

The volume of the pyramid is approximately 1.3 square meters.