Chapter 7, Problem 49P

To determine

Find the frontal area of the cell phone by excluding the display panel in SI unit and U.S. Customary unit.

Answer to Problem 49P

The frontal area of the cell phone by excluding the display panel in SI unit and U.S. Customary unit is $0.0057{\text{m}}^2$ and $0.06156{\text{ft}}^2$.

Explanation of Solution

Given data:

The height of the cell phone $\left(H\right)$ is $13\text{cm}$,

The width of the cell phone $\left(W\right)$ is $8\text{cm}$.

Formula used:

Formula to calculate the frontal area of the cell phone by excluding the display panel is,

$A=A_1-A_2$ (1)

Here,

$A_1$ is the total frontal area of the cell phone,

$A_2$ is the area of the display panel.

Calculation:

Total frontal area:

Formula to calculate the total frontal area of the cell phone is,

$A_1=H\times W$ (2)

Here,

$H$ is height of the cell phone,

$W$ is width of the cell phone.

Substitute $13\text{cm}$ for $H$, and $8\text{cm}$ for $W$ in equation (2) to find $A_1$.

$\begin{array}{c}{A}_1=\left(13\text{cm}\right)\times \left(8\text{cm}\right)\\ =104{\text{cm}}^2\end{array}$

Area of the display panel:

Refer to the figure 7.49, the height and width of the cell phone is divided as slots. Therefore,

$\text{The height of the cell phone = 13 cm = 18 slots}$

For 1 slot, the height is:

$1\text{slot}=\frac{13}{18}\text{cm}$

$\text{The width of the cell phone}=\text{8 cm}=\text{11 slots}$

For 1 slot, the width is:

$1\text{slot}=\frac{8}{11}\text{cm}$

From the figure 7.49, approximately the number of slots in height of the display panel is 10, and in width of the display panel is 9.

Substitute the respective slot values in cm for the height and width of the cell phone.

$\begin{array}{c}\text{The height of the display panel}\left(h\right)\text{ = 10 slots}\\ \text{= }\left(\text{10}\right)\left(\frac{13}{18}\text{cm}\right)\\ =7.22\text{cm}\end{array}$

$\begin{array}{c}\text{The width of the display panel }\left(w\right)\text{= 9 slots}\\ \text{= }\left(\text{9}\right)\left(\frac{13}{18}\text{cm}\right)\\ =6.5\text{cm}\end{array}$

Formula to calculate the area of the display panel is,

$A_2=h\times w$ (3)

Here,

$h$ is height of the display panel,

$w$ is width of the display panel.

Substitute $7.22\text{cm}$ for $h$, and $6.5\text{cm}$ for $w$ in equation (3) to find $A_2$.

$\begin{array}{c}{A}_2=\left(7.22\text{cm}\right)\times \left(6.5\text{cm}\right)\\ =47{\text{cm}}^2\end{array}$

Substitute $104{\text{cm}}^2$ for $A_1$ and, $47{\text{cm}}^2$ for $A_2$ in equation (1) to find $A$.

$\begin{array}{c}A=\left(104{\text{cm}}^2\right)-\left(47{\text{cm}}^2\right)\\ =57{\text{cm}}^2\end{array}$

The SI unit of the frontal area by excluding the display panel is,

$\begin{array}{c}A=57{\text{cm}}^2\left[\therefore 1{\text{cm}}^2=\text{0}\text{.0001}{\text{m}}^2\right]\\ =57\left(\text{0}\text{.0001}{\text{m}}^2\right)\\ =0.0057{\text{m}}^2\end{array}$

The U.S. Customary unit of the frontal area by excluding the display panel is,

$\begin{array}{c}A=57{\text{cm}}^2\left[\therefore 1{\text{cm}}^2=\text{0}\text{.00108}{\text{ft}}^2\right]\\ =57\left(\text{0}\text{.00108}{\text{ft}}^2\right)\\ =0.06156{\text{ft}}^2\end{array}$

Therefore, the frontal area of the cell phone by excluding the display panel in SI unit and U.S. Customary unit is $0.0057{\text{m}}^2$ and $0.06156{\text{ft}}^2$.

Conclusion:

Thus, the frontal area of the cell phone by excluding the display panel in SI unit and U.S. Customary unit is $0.0057{\text{m}}^2$ and $0.06156{\text{ft}}^2$.