Question

A box is shaped like an octagonal prism. Here is what the base of the prism looks like. If the height of the box is 7 inches, the volume of the box will be [1] cubic inches.

Answer 1

Answer:

The volume of the box is 33.796 cubic inches

Step-by-step explanation:

Given

$Height = 7in$

See attachment for the base of the prism

Required

The volume of the box

From the attachment, we have:

$a = 1in$ -- side length of the octagon

The area is then calculated as:

$Area = 2 * (1 + \sqrt 2)a^2$

So, we have:

$Area = 2 * (1 + \sqrt 2)* 1^2$

$Area = 2 * (1 + \sqrt 2)* 1$

$Area = 2 * (1 + \sqrt 2)$

Evaluate the square root

$Area = 2 * (1 + 1.414)$

$Area = 2 * (2.414)$

$Area = 4.828$

The volume is then calculated as:

$Volume = Height * Base\ Area$

$Volume = 7 * 4.828$

$Volume = 33.796$

Answer 2

Answer:

287 is the right answer

Step-by-step explanation:

Hopes this helps.