Dimensional Analysis Problem Help

Question

A cape is designed for Lady Gaga's concert with 4,560 sequins. If a sequin has a volume of 0.0241 cm3 and the sequins have a density of 681.7 g/in3, what is the mass in lb of the sequins on Lady Gaga's cape?

Answer 1

Find the volume of the sequins:

4560 sequins x 0.0241 cm³/sequin = 109.896 cm³

Convert the density given in g/in³ to g/cm³

Since 1 inch = 2.54 cm, we have 2.54 cm x 2.54 cm x 2.54 cm = 16.387 cm³ = 1in³

Density = 681.7 g/in³ x 1in³/16.387cm³ = 41.60 g/cm³

Find the mass in g using the volume and the density:

109.896 cm³ x 41.60 g/cm³ = 4572 g

Convert grams to lbs using the conversion factor of 454 g = 1 lb

4572 g x 1 lb/454 g = 10.0 lbs (to 3 significant figures)