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]
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]
