Question

To the nearest cubic centimeter, what is the volume of the regular hexagonal prism?

Answer 1

The volume is 164cm^3

Explanation:

Given

`h = 7` --- height

`a = 3` --- base length

`r = 2.6`

Required

The volume

The volume (V) is calculated as:

`V = (3\sqrt 3)/(2)a^2h`

This gives:

`V = (3\sqrt 3)/(2) * 3^2 * 7`

`V = (3\sqrt 3)/(2) * 9 * 7`

`V = (3\sqrt 3)/(2) * 63`

`V = (3*1.7321)/(2) * 63`

Using a calculator, we have:

`V = 163.68`

Approximate

`V = 164cm^3`