Chapter 12.8, Problem 7OE

To determine

To Describe: Translate the statement into formula:

The total force , $F$ , of a liquid varies jointly as the area of surface , $A$ , the depth of liquid, $h$ , and density $d$,

Answer to Problem 7OE

The formula of the statement is $F=KAhd$ .

Explanation of Solution

Given information:

Translate statement to formula:

The total force , $F$ , of a liquid varies jointly as the area of surface , $A$ , the depth of liquid, $h$ , and density $d$ ,

Use $K$ as constant.

Consider the statement,

The total force , $F$ , of a liquid varies jointly as the area of surface , $A$ , the depth of liquid, $h$ , and density $d$ ,

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

As , $F$ ,varies jointly to $A,h,d$ .

  $F$ is jointly with $A$ .

  $F\alpha A$ .

Then $F$ is jointly with $h$ .

  $F\alpha h$

Now $F$ is jointly with $d$ .

  $F\alpha d$

From all three equations:

  $\begin{array}{c}F\alpha A\\ F\alpha h\\ F\alpha d\\ F\alpha Ahd\end{array}$

Same as above,

Here,

  $F\alpha Ahd$

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

  $\begin{array}{l}F\alpha Ahd\\ F=KAhd\end{array}$

Thus, the formula is: $F=KAhd$ .