Respuesta :
Answer:
[tex]V=42.7m^3[/tex]
Step-by-step explanation:
The volume of a square pyramid is given by the equation:
[tex]V=\frac{A_{b}h}{3}[/tex]
where [tex]A_b[/tex] is the area of the base, in this case the area of the square. And h is the height of the pyramid:
[tex]h=12.5m[/tex]
To find the area of the square we need the length of its sides, which can be found dividing the perimeter by four.
The perimeter is:
[tex]p=12.8m[/tex]
thus, the length of the side is:
[tex]l=\frac{p}{4} =\frac{12.8m}{4}=3.2m[/tex]
and the area of square at the base is then given by the formula:
[tex]A_b=l^2\\\\A_b=(3.2m)^2\\\\A_b=10.24m^2[/tex]
Finally we substitute all the known values into the equation for the volume:
[tex]V=\frac{A_{b}h}{3}[/tex]
[tex]V=\frac{(10.24m^2)(12.5m)}{3}\\ \\V=\frac{128m^3}{3}\\ \\V=42.667m^3[/tex]
rounding the volume to the nearest tenth of a cubic meter:
[tex]V=42.7m^3[/tex]
