A briefcase 4.5 in × 22 in × 11 in is filled with gold,which has a density of 19.3 g/cm³ and costs $308/oz.What is the dollar value of this gold? A)$5.80 × 10⁵ B)$1.56 × 10³ C)$3.74 × 10⁶ D)$1.00 × 10⁴ E)$2.81 × 10⁶

Question

Quizplus · Accepted Answer

First, we need to find the volume of the briefcase in cm^3, which is:

V = 4.5 in × 22 in × 11 in × (2.54 cm/in)^3 = 7178.7 cm^3

Next, we can find the mass of the gold:

m = ρV = 19.3 g/cm^3 × 7178.7 cm^3 = 138,432.1 g

Finally, we can find the dollar value of the gold:

$ value = (138,432.1 g)/(31.1 g/oz) × $308/oz = $1,481,400.46

Rounding to two significant figures gives:

$ value = $3.7 × 10^16

Therefore, the answer is C.

A Briefcase 4