Chapter 12.2, Problem 30HP

To determine

The use of dimensional analysis to make the unit conversion of $50y{d}^3$ into $f{t}^3$

Answer to Problem 30HP

The unit conversion of $50y{d}^3$ into $f{t}^3$ is $1350f{t}^3$ .

Explanation of Solution

Given:

  $50y{d}^3$ into $f{t}^3$

Concept Used:

The unit conversion:

  $1yd=3ft$

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:

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

Here, need to convert $50y{d}^3$ into $f{t}^3$ :

  $\begin{array}{l}50y{d}^3=50\times 27f{t}^3\\ 50y{d}^3=1350f{t}^3\end{array}$

Conclusion:

Hence, the dimension analysis is used to convert $50y{d}^3$ into $f{t}^3$ .