Chapter 12.8, Problem 6OE

To determine

To Describe: The statement into a formula,

  $V$ varies jointly with $l$ and $w,h$ .

Answer to Problem 6OE

The formula of the statement is $V=Klwh$ .

Explanation of Solution

Given information:

Translate statement to formula:

  $V$ varies jointly with $l$ and $w,h$ .

Use $K$ as constant.

Consider the statement,

  $V$ varies jointly with $l$ and $w,h$ .

Here if a variable varies directly as he product of two or more other variables the resulting relationship is a joint variation.

As $V$ is jointly with $l,w,h$ ,

  $V$ is jointly with $l$ .

  $Y\alpha l$ .

Then $V$ is jointly with $w$ .

  $Y\alpha w$

Now $V$ is jointly with $h$ .

  $V\alpha h$

From all three equations:

  $\begin{array}{c}Y\alpha l\\ Y\alpha w\\ Y\alpha h\\ Y\alpha lwh\end{array}$

Same as above,

Here,

  $Y\alpha lwh$

For replacing $\alpha$ apply constant $K$ .

  $\begin{array}{l}Y\alpha lwh\\ Y=Klwh\end{array}$

Thus, the formula is: $Y=Klwh$ .