Chapter 12.8, Problem 16PPS

a.

To determine

The scale factor of the prisms.

Answer to Problem 16PPS

  $4:5$

Explanation of Solution

Given:

Two suitcases are similar rectangular prisms.

The smaller suitcase is 68 centimeters long, 47 centimeters wide and 27 centimeters deep.

The larger suitcase is 85 centimeters long.

Calculation:

From the given information, the scale factor of their side length is,

  $\Rightarrow 68:85$

Simplifying to lowest terms,

  $\Rightarrow 4:5$

Conclusion:

Therefore, the scale factor of the prisms is $4:5.$

b.

To determine

To determine the volume of the larger suitcase.

Answer to Problem 16PPS

  $168539.1{\text{ centimeter}}^3$

Explanation of Solution

Given:

Two suitcases are similar rectangular prisms.

The smaller suitcase is 68 centimeters long, 47 centimeters wide and 27 centimeters deep.

The larger suitcase is 85 centimeters long.

Formula used:

Volume of the prism $=lwh$

  $\left[l=\text{length , }w=\text{width and }h=\text{height}\right]$

Calculation:

From the previous part scale factor of the prisms is $4:5.$

Finding the value of volume of smaller prism,

Volume of the prism $=lwh$

  $\Rightarrow \text{The volume of the smaller suitcase}=68\times 47\times 27$

  $=86292{\text{ centimeter}}^3$

Now, writing a proportion to find the volume of greater circle.

Ratio of volume can be given by,

  $\Rightarrow \frac{4^3}{5^3}=\frac{86292}{V}\left[V=\text{volume of larger suitcase}\right]$

Cross multiplying,

  $\Rightarrow 64V=10786500$

  $\Rightarrow V=\frac{10786500}{64}$

  $\Rightarrow V=168539.1{\text{ centimeter}}^3$

Conclusion:

Therefore, the volume of the larger suitcase is $168539.1{\text{ centimeter}}^3$ .