Answer:
[tex]V=18.2cm^3[/tex]
Step-by-step explanation:
The volume of the pyramid is given by:
[tex]V=\frac{A_{b}h}{3}[/tex]
where [tex]A_{b}[/tex] is the area of the base and [tex]h[/tex] is the height.
We know that the height is:
[tex]h=13cm[/tex]
Thus we need to find the area of the square at the base.
The perimeter of the square is:
[tex]p=8.2cm[/tex]
this means that the length of the sides of the square is :
[tex]l=\frac{p}{4}\\ \\l=\frac{8.2cm}{4}\\ \\l=2.05cm[/tex]
Now we can find the area of the base which the area of the square:
[tex]A_{b}=l^2\\A_b=(2.05cm)^2\\A_b=4.2025cm^2[/tex]
and finally we find the volume:
[tex]V=\frac{A_{b}h}{3}[/tex]
[tex]V=\frac{(4.2025cm^2)(13cm)}{3}\\ \\V=\frac{54.6325cm^3}{3}\\ \\V=18.2108cm^3[/tex]
Which rounded to the nearest tenth of a cubic centimeter is: [tex]V=18.2cm^3[/tex]
