Question

Find the missing dimension of the prism. Round your answer to the nearest hundredth.

Volume = 72.66 in.?

Х

2 in.

Answer 1

`x = 6.99in`

Explanation:

Given

`l =2in`

`Volume = 72.66in^3`

See attachment for prism

Required

Find x

The prism has a regular hexagon base

The base area is calculated as:

`Base\ Area= (3\sqrt 3)/(2)l^2`

This gives:

`Base\ Area= (3\sqrt 3)/(2) * 2^2`

`Base\ Area= (3\sqrt 3)/(2) * 4`

`Base\ Area= 3\sqrt 3 * 2`

`Base\ Area= 6\sqrt 3`

Side x represents the height.

So, we have:

`Volume = Base\ Area*x`

Make x the subject

`x = (Volume )/( Base\ Area)`

`x = (72.66in^3)/(6\sqrt 3 in^2)`

`x = (72.66)/(6\sqrt 3)in`

`x = (12.11)/(\sqrt 3)in`

`x = 6.99in` --- approximated