The density of a subtance can be found by dividing the mass of the substance by the volume of the substance. The table gives the density of several pure metals in grams per cubic centimeter. Suppose a rectangular sheet of a pure metal weights about 515.9 grams and measures `(1)/(4)` inch by 2 inches by 8 inches. Assuming the sheet is one of the metals in the table, which metal is it? (There are approximately 2.54 centimeters in 1 inch.)

Options

A. Copper
B. Iron
C. Nickel
D. Tin

Answer

B

Explanation

Difficult: Medium
Category: Problem Solving and Data Analysis/ Rates, Ratios, Proportions, and Percentages
Strategic Advice: Always pay careful attention to units. When converting from a linear measure, such as inches, to cubic measure, such as `cm^(3)` (or vice versa), you will need to write three units conversions.
Getting to the Answer:Start by finding the valume of the metal sheet using the formula `V=lwh`. The volume is `(1)/(4)times2times8=4` cubic inches. Now, carefully convert this to cubic centimeters:
`4"in"^(3)times(2.54cm)/(1"in")times(2.54cm)/(1"in")times(2.54cm)/(1"in")=65.55cm^(3)`
Skim the question again: To find the density of the metal, divide the mass (given in the question) by the volumes : 515.9/65.55=7.87, which matches the density of iron, (B).