Chapter 11.2, Problem 22P

A rectangular prism has a base area of $3x^2+21x-24$ and a height of $\frac{x}{33x-33}$.

What is the volume of the prism?

To determine

To find : the volume of the prism

Answer to Problem 22P

The volume of the prism is $\frac{x\left(x+8\right)}{11}$

Explanation of Solution

Given information : A rectangular prism has a base area of $3x^2+21x-24$ and a height of $\frac{x}{33x-33}$

Formula used : $volume=area\times height$

Calculation :

Base area $=3x^2+21x-24$

Height of length $=\frac{x}{33x-33}$

  $volume=area\times height$

  $\begin{array}{l}V=\left(3x^2+21x-24\right)\times \left(\frac{x}{33x-33}\right)\\ V=\frac{\left(x+8\right)\left(3x-3\right)x}{11\left(3x-3\right)}\\ V=\frac{x\left(x+8\right)}{11}\end{array}$