# The dimensions for a rectangular prism are x+5 for the length, x+1 for the width, and x for the height. What is the volume of the prism?

Nov 3, 2016

$v = {x}^{3} + 6 {x}^{2} + 5 x$

#### Explanation:

The formula for volume is: $v = l \cdot w \cdot h$ where $v$ is the volume, $l$ is the length, $w$ is the width and $h$ is the height.

Substituting what we know into this formula gives:

$v = \left(x + 5\right) \left(x + 1\right) x$

$v = \left(x + 5\right) \left({x}^{2} + x\right)$

$v = {x}^{3} + {x}^{2} + 5 {x}^{2} + 5 x$

$v = {x}^{3} + \left(1 + 5\right) {x}^{2} + 5 x$

$v = {x}^{3} + 6 {x}^{2} + 5 x$