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 calculate the volume of the briefcase:

Volume = (4.5 in)(22 in)(11 in) = 1089 in3

Then, we need to convert the density to units of dollars per cubic inch:

19.3 g/cm3 = 0.7008 oz/in3 (since 1 g/cm3 = 0.03527 oz/in3)

Next, we can calculate the total amount of gold in the briefcase:

Amount of gold = (0.7008 oz/in3)(1089 in3) = 764.77 oz

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

Dollar value = (764.77 oz)($308/oz) = $2.3611 x 1013 or $3.74 × 1016 (in scientific notation with proper significant figures)

Therefore, the best choice is C.

A Briefcase 4