Question

a machinist creates a solid steel part for an engine. the part has a volume of 1015 cubic centimeters. steel can be purchased for $0.29 per kilogram, and has a density of \\(\frac{0.00795\\ \text{kg}}{\text{cm}^3}\\). if the machinist makes 500 of these parts, what is the cost of the steel, to the nearest dollar?

Explanation:

Step1: Find mass of one part

Mass = Density × Volume
$m = 0.00795\ \frac{\text{kg}}{\text{cm}^3} \times 1015\ \text{cm}^3 = 8.06925\ \text{kg}$

Step2: Find mass of 500 parts

Total mass = Mass per part × 500
$M = 8.06925\ \text{kg} \times 500 = 4034.625\ \text{kg}$

Step3: Calculate total cost

Total cost = Total mass × Cost per kg
$C = 4034.625\ \text{kg} \times 0.29\ \frac{\$}{\text{kg}} = 1170.04125$

Step4: Round to nearest dollar

Round the total cost to whole number
$\text{Rounded cost} = \text{round}(1170.04125)$

Answer:

1170