Inches Long
How many inches long must the section of bar be?
A standard 1.000 kg mass is to be cut from a bar of steel having an equilateral triangular cross section with sides equal to 2.20 in. The density of the steel is 7.70 g/cm^3.
How many inches long must the section of bar be?
This problem requires conversion and a little bit of algebra.
The first step you want to do is solve for the volume of the bar. You can do this by dividing the mass by the density. Since you have different units for mass and density, you need to convert 1.000 kg to g.
We know that there are 1000 g in 1 kg. So we will use this equation to solve for volume.
1000 g / 7.700 g/cm³ = 129.9 cm³
Now you will have to convert your volume to cubic inches (because the question is asking for length in inches). We know that 1 inch³ = 16.4 cm³. Do another division problem to get your volume in cubic inches.
129.9 cm³ / 16.4 cm³ = 7.92 inch³
Now that you have the volume in inch³ we need to remember some algebra.
volume = area * length
If we can solve for the area of the triangle then all we have to do is divide the volume by that area to get the length. We are told that the cross section of this bar is an equilateral triangle with sides of 2.20 inch. We can use this formula (modified from the pythagoras theorem) to get the area.
area = (√3 / 4) * (2.2 * 2.2)
This should give you an area of 2.10 inches.
Divide your volume by your area to get the length.
7.92 / 2.10 = 3.77 inches
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