1. ## Measurements

I love measurements, but I really didn't have time to do these until now, 3 hours before the class.

1- The avarage density of Styrofoam is 1.00 kg/$\displaystyle m^3$. If a Styrofoam cooler is made with outside dimensions of 20.0 * 14.0 * 12.0 inches and the uniform thikcness of the Styrofoam is 1.50 inches ( including the lid ), what is the volume of the Styrofoam used in cubic meters? What is the mas in kilograms? How many gallons of liquid could be stored in the cooler?

2- A pressure gauge on an air tank reads 210 pounds per square inch (psi). The face on the gauge says +_ 3% at 180 psi.
a) What is the range of air pressure in the tank when the gauge reads 210 psi ?
b) What is it when the gauge reads 87 psi ?

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- this star * in the first problem means " multiply by"
- +_ , these two signs are supposed to be over each other but i don't know how to do it.

and the book answers to the problems are :
1 - volume = 2.75 * $\displaystyle 10^-2$ $\displaystyle m^3$
Mass = 2.75 * $\displaystyle 10^-2$ kg
# gal = 7.29 gal

2 -
a) 205-215 lb/$\displaystyle in^2$
b) 82-92 lb/$\displaystyle in^2$

$\displaystyle 10^-2$ is 10 to the power -2

2. Originally Posted by Apathetic
I love measurements, but I really didn't have time to do these until now, 3 hours before the class.

1- The avarage density of Styrofoam is 1.00 kg/$\displaystyle m^3$. If a Styrofoam cooler is made with outside dimensions of 20.0 * 14.0 * 12.0 inches and the uniform thikcness of the Styrofoam is 1.50 inches ( including the lid ), what is the volume of the Styrofoam used in cubic meters? What is the mas in kilograms? How many gallons of liquid could be stored in the cooler?
The outside volume (volume enclosed by the outer surface) is:

$\displaystyle 20.0 \times 14.0 \times 12.0= 3360 \text{ cubic inches}$

The inside dimensions are all $\displaystyle 3$ inches smaller, so the inside volume is:

$\displaystyle 17.0 \times 11.0 \times 9.0= 1683 \text{ cubic inches}$

The volume of foam is the difference between these. The conversion factor from cubic inches to metres is:

$\displaystyle 1.6387 \times 10^{-5} \text{ cubic meters/cubic inch}$.

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