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Chapter 1: Problem 53

Aluminum is a lightweight metal (density \(=2.70 \mathrm{~g} / \mathrm{cm}^{3}\) ) used in aircraft construction, high-voltage transmission lines, beverage cans, and foils. What is its density in \(\mathrm{kg} / \mathrm{m}^{3} ?\)

Short Answer

Expert verified
The density of aluminum in kilograms per cubic meter is \(2700 \, \mathrm{kg/m}^3\).

Step by step solution

01

Understand the relationship between the units

First, understand that 1 gram is equivalent to 0.001 kilogram and 1 cubic centimeter is equivalent to \(1 \times 10^{-6}\) cubic meter.
02

Conversion of density from g/cm^3 to kg/m^3

It's now time to perform the conversion. Since 1 gram equals 0.001 kilogram and 1 cubic centimeter is \(1 \times 10^{-6}\) cubic meter, one can multiply 2.70 g/cm^3 by these conversion factors. This calculation would look like \(2.70 \, \mathrm{g/cm}^3 \times \frac{0.001 \, \mathrm{kg}}{1 \, \mathrm{g}} \times \frac{1}{1 \times 10^{-6} \, \mathrm{m}^3/\mathrm{cm}^3}\)
03

Calculate

Now, simplify the operation for the final answer. The grams and cubic centimeters will cancel out to leave the density in kilograms per cubic meter, giving the outcome.

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Most popular questions from this chapter

The average speed of helium at \(25^{\circ} \mathrm{C}\) is \(1255 \mathrm{~m} / \mathrm{s}\) Convert this speed to miles per hour (mph).

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