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The pressure inside a tire is measured as [tex]28.0 \frac{\text{pounds}}{\text{inch}^2}[/tex]. What is its pressure in [tex]\frac{\text{newtons}}{\text{centimeter}^2}[/tex]?

1 pound [tex]= 4.45[/tex] newtons

1 inch[tex]^2 = 6.45[/tex] centimeters[tex]^2[/tex]

Express the answer to the correct number of significant figures.

The pressure is [tex]\square \frac{\text{newtons}}{\text{centimeter}^2}[/tex].



Answer :

To find the pressure in newtons per centimeter cubed when the pressure inside a tire is given as 28.0 pounds per inch squared, we need to perform unit conversions step by step.

1. Convert pounds per inch squared to newtons per centimeter squared:

- Given:
[tex]\[ \text{Pressure} = 28.0 \frac{\text{pounds}}{\text{inch}^2} \][/tex]
- Conversion factors:
[tex]\[ 1 \text{ pound} = 4.45 \text{ newtons} \][/tex]
[tex]\[ 1 \text{ inch}^2 = 6.45 \text{ centimeters}^2 \][/tex]

- Convert pressure to newtons per centimeter squared:
[tex]\[ \text{Pressure in newtons per cm}^2 = 28.0 \frac{\text{pounds}}{\text{inch}^2} \times \frac{4.45 \text{ newtons}}{1 \text{ pound}} \times \frac{1 \text{ inch}^2}{6.45 \text{ centimeters}^2} \][/tex]

2. Calculate this value:
[tex]\[ \text{Pressure in newtons per cm}^2 = 28.0 \times \frac{4.45}{6.45} \][/tex]
[tex]\[ \text{Pressure in newtons per cm}^2 \approx 19.317829457364343 \][/tex]

3. Convert newtons per centimeter squared to newtons per centimeter cubed:

Since \(1 \text{ centimeter}^2\) is equal to \(10 \text{ centimeter}^3\) (assuming a linear dimension conversion requires multiplication by 10 as part of the conversion):
[tex]\[ \text{Pressure in newtons per cm}^3 = \frac{\text{Pressure in newtons per cm}^2}{10} \][/tex]
[tex]\[ \text{Pressure in newtons per cm}^3 \approx \frac{19.317829457364343}{10} \][/tex]
[tex]\[ \text{Pressure in newtons per cm}^3 \approx 1.9317829457364344 \][/tex]

4. Report the final answer to the correct number of significant figures:

The given data has three significant figures (28.0, 4.45, and 6.45). Therefore, we should report our answer to three significant figures.

[tex]\[ \text{The pressure is } \boxed{1.93} \frac{\text{newtons}}{\text{centimeter}^3} \][/tex]