Question

Express the statement as an equation. Use the given information to find the constant of proportionality.

C is jointly proportional to l, w, and h. If $l=w=h=2$, then $C=128$.

Short answer

Equation that represents the statement is $C=k\left(l\times w\times h\right)$.

Constant of proportionality is 16.

Step-by-step solution

Step 1. Understanding Direct variation.

Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other.

For example:

$y=kx$

Now, if x and z are jointly proportional to y, then,

$y=k\left(xz\right)$

Here $k\ne 0$, y is directly proportional to x and vice versa.

Step 2. Write the equation.

As C is jointly proportional to x and y, hence

$C=k\left(l\times w\times h\right)$

Where k is constant of proportionality.

Step 3. Plug the values given in the equation to determine the value of the constant of proportionality.

Given values:

$l=w=h=2$

Putting values we get,

$\begin{array}{l}128=k\left(2\times 2\times 2\right)\\ 128=8k\\ k=16\end{array}$