Chapter 12.8, Problem 19PPS

To determine

To determine the height of Mateo’s player.

Answer to Problem 19PPS

  $h=4.1\text{ inch}$

Explanation of Solution

Given:

The players are congruent rectangular prisms.

The volume of Jalissa’s player is 4.92 cubic inches, the width is 2.4 inches, and the depth is 0.5 inch.

Formula used:

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

Calculation:

If the shapes are congruent then the scale factor ratio is same.

Since the rectangular prisms are congruent, then there scale factor is 1:1.

Both rectangular prisms have the same length, width, and height.

Let’s consider height of Mateo’s player be $h$ .

Then volume of Jalissa’s player is same as Mateo’s player,

  $\Rightarrow$ Volume of Jalissa’s player $=$ Volume of Mateo’s player

  $\Rightarrow 4.92=2.4\times 0.5\times h$

  $\Rightarrow 4.92=2.4\times 0.5\times h$

  $\Rightarrow h=\frac{4.92}{2.4\times 0.5}$

  $\Rightarrow h=4.1\text{ inch}$

Conclusion:

Therefore, the height of Mateo’s player is $h=4.1\text{ inch}$ .