Answer:
The volume of the box is 33.796 cubic inches
Step-by-step explanation:
Given
[tex]Height = 7in[/tex]
See attachment for the base of the prism
Required
The volume of the box
From the attachment, we have:
[tex]a = 1in[/tex] -- side length of the octagon
The area is then calculated as:
[tex]Area = 2 * (1 + \sqrt 2)a^2[/tex]
So, we have:
[tex]Area = 2 * (1 + \sqrt 2)* 1^2[/tex]
[tex]Area = 2 * (1 + \sqrt 2)* 1[/tex]
[tex]Area = 2 * (1 + \sqrt 2)[/tex]
Evaluate the square root
[tex]Area = 2 * (1 + 1.414)[/tex]
[tex]Area = 2 * (2.414)[/tex]
[tex]Area = 4.828[/tex]
The volume is then calculated as:
[tex]Volume = Height * Base\ Area[/tex]
[tex]Volume = 7 * 4.828[/tex]
[tex]Volume = 33.796[/tex]
