Question

a student has samples of five different types of metal. she measures the mass and volume of each sample. the measurements she took are in the table.

type of metal	mass (g)	volume (cm³)
iron	33.1	4.2
lead	35.2	3.1
magnesium	10.6	6.1
silver	47.2	4.5

the student also has another piece of metal. she knows it is the same type of metal as one of her other samples, but she doesnt know which one it is. she finds that its mass is 33.5 grams and its volume is 3.2 centimeters³. what type of metal is the unknown sample?

a. aluminum 2.70
b. iron 7.87
c. lead 11.34
d. magnesium 1.74
e. silver 10.49

Explanation:

Step1: Recall density formula

Density \(
ho = \frac{\text{mass}}{\text{volume}} \). We need to calculate the density of the unknown sample and compare it with the densities of the given metals.

Step2: Calculate unknown density

For the unknown sample, mass \( m = 33.5 \, \text{g} \), volume \( V = 3.2 \, \text{cm}^3 \). So density \(
ho = \frac{33.5}{3.2} \approx 10.47 \, \text{g/cm}^3 \).

Step3: Calculate densities of given metals

• Aluminum: \( \frac{14.6}{5.4} \approx 2.70 \, \text{g/cm}^3 \)
• Iron: \( \frac{33.1}{4.2} \approx 7.88 \, \text{g/cm}^3 \)
• Lead: \( \frac{35.2}{3.1} \approx 11.35 \, \text{g/cm}^3 \)
• Magnesium: \( \frac{10.6}{6.1} \approx 1.74 \, \text{g/cm}^3 \)
• Silver: \( \frac{47.2}{4.5} \approx 10.49 \, \text{g/cm}^3 \)

Step4: Compare unknown density

The unknown density (\( \approx 10.47 \)) is closest to silver's density (\( \approx 10.49 \)).

Answer:

E. silver 10.49