Chapter 12.2, Problem 31HP

To determine

The use of dimensional analysis to make the unit conversion of $945f{t}^3$ into $y{d}^3$

Answer to Problem 31HP

The unit conversion of $945f{t}^3$ into $y{d}^3$ is $35y{d}^3$ .

Explanation of Solution

Given:

  $945f{t}^3$ into $y{d}^3$

Concept Used:

The unit conversion:

  $1ft=\frac{1}{3}yd$

Calculation:

In the given eg:

There is cube of the unit is taken so need to take the cube on the both sides of unit conversion formula:

  $\begin{array}{l}1ft=\frac{1}{3}yd\\ 1f{t}^3=\frac{1}{{\left(3\right)}^3}y{d}^3\\ 1f{t}^3=\frac{1}{27}y{d}^3\end{array}$

Here, need to convert $945f{t}^3$ into $y{d}^3$ :

  $\begin{array}{l}945f{t}^3=945\times \frac{1}{27}y{d}^3\\ 945f{t}^3=35y{d}^3\end{array}$

Conclusion:

Hence, the dimension analysis is used to convert $945f{t}^3$ into $y{d}^3$ .