Question

1. infer yuri conducted an experiment on three metal samples. she created the table below from the data she collected.

table 2 | densities of samples

sample	mass	volume
2	1.93 g	1.11 cm³
3	6.10 g	2.26 cm³

table 3 | density table

metal	density (g/cm³)
copper	8.96
lead	11.35
iron	7.87
magnesium	1.74
zinc	7.13

use table 3 to identify each sample in table 2. teks 6.2b, 6.2c, 6.5d
a sample #1 is copper; sample #2 is magnesium; sample #3 is lead.
b sample #1 is iron; sample #2 is magnesium; sample #3 is aluminum.
c sample #1 is iron; sample #2 is aluminum; sample #3 is copper.
d sample #1 is zinc; sample #2 is lead; sample #3 is aluminum.

Explanation:

Step1: Recall density formula

Density formula is $
ho = \frac{m}{V}$, where $
ho$ is density, $m$ is mass, and $V$ is volume.

Step2: Calculate density for Sample 1

For Sample 1: $m = 33.8\ g$, $V = 2.26\ cm^3$.
$
ho_1 = \frac{33.8}{2.26} \approx 14.96$? Wait, no, wait, maybe miscalculation. Wait, 33.8 divided by 2.26: let's do 33.8 ÷ 2.26. 2.26×14 = 31.64, 33.8 - 31.64 = 2.16, 2.16/2.26 ≈ 0.955, so total ≈14.95? No, that can't be. Wait, maybe I misread the mass. Wait, Table 2: Sample 1 mass is 33.8 g? Wait, no, maybe it's 37.8? Wait, the handwritten note is 2.26√37.8? Oh, maybe the mass is 37.8 g? Wait, the original table: Sample 1 mass 33.8 g? Wait, no, maybe a typo. Wait, let's check again. Wait, the user's image: Table 2, Sample 1: Mass 33.8 g, Volume 2.26 cm³. Sample 2: 1.93 g, 1.11 cm³. Sample 3: 6.10 g, 2.26 cm³. Table 3: Aluminum 2.70, Copper 8.96, Lead 11.35, Iron 7.87, Magnesium 1.74, Zinc 7.13.

Wait, let's recalculate Sample 1: 33.8 / 2.26 ≈ 14.95? That's not in Table 3. Wait, maybe the mass is 37.8? Because the handwritten is 2.26√37.8. Let's assume that's a typo, and mass is 37.8 g. Then 37.8 / 2.26 ≈ 16.7? No, still not. Wait, no, maybe I messed up. Wait, Sample 3: 6.10 g / 2.26 cm³ ≈ 2.698 ≈ 2.70, which is Aluminum. Ah! So Sample 3: 6.10 / 2.26 ≈ 2.698 ≈ 2.70 (Aluminum). Then Sample 2: 1.93 / 1.11 ≈ 1.738 ≈ 1.74 (Magnesium). Sample 1: 33.8 / 2.26 ≈ 14.95? No, wait, 33.8 / 2.26: 2.26×14 = 31.64, 33.8 - 31.64 = 2.16, 2.16/2.26 ≈ 0.955, so 14.95. But Table 3 has Lead 11.35, Copper 8.96, Iron 7.87, Zinc 7.13. Wait, maybe the mass is 33.8? No, maybe I made a mistake. Wait, Sample 3: 6.10 / 2.26 ≈ 2.698 ≈ 2.70 (Aluminum). So Sample 3 is Aluminum. Then look at options: Option B says Sample #3 is aluminum. Option B: Sample #1 is iron (7.87), Sample #2 is magnesium (1.74), Sample #3 is aluminum (2.70). Let's check Sample 1: 33.8 / 2.26 ≈ 14.95? No, that's not iron. Wait, maybe the mass is 37.8? 37.8 / 2.26 ≈ 16.7? No. Wait, maybe the volume is 4.26? No. Wait, maybe I miscalculated Sample 1. Wait, 33.8 divided by 2.26: let's do 33.8 ÷ 2.26. 2.26 × 14 = 31.64, 33.8 - 31.64 = 2.16, 2.16 ÷ 2.26 ≈ 0.955, so total ≈14.95. But Table 3 has no metal with density ~15. Wait, maybe the mass is 33.8, volume 4.26? No. Wait, maybe the problem has a typo, but let's check the options. Option B: Sample 1 iron (7.87), so 7.87 × 2.26 ≈ 17.79 g, but Sample 1 mass is 33.8 g. No. Wait, Sample 3: 6.10 / 2.26 ≈ 2.70 (Aluminum), so Sample 3 is Aluminum. So options with Sample 3 as Aluminum: B and D. D says Sample 3 is aluminum, but Sample 2 is lead (11.35), 1.93 / 1.11 ≈ 1.74 ≠ 11.35. So D is wrong. B: Sample 2 is magnesium (1.74), 1.93 / 1.11 ≈ 1.738 ≈ 1.74 (correct). Sample 3 is aluminum (2.70), 6.10 / 2.26 ≈ 2.698 ≈ 2.70 (correct). Sample 1: iron (7.87), so mass should be 7.87 × 2.26 ≈ 17.79 g, but Sample 1 mass is 33.8 g. Wait, that's a problem. Wait, maybe I misread Sample 1's mass. Wait, maybe it's 37.8 g? 37.8 / 2.26 ≈ 16.7, no. Wait, maybe the volume is 4.26? 33.8 / 4.26 ≈ 7.93 ≈ 7.87 (iron). Ah! Maybe the volume of Sample 1 is 4.26 cm³, not 2.26? But the table says 2.26. Wait, maybe a typo. Alternatively, maybe the mass is 17.79 g, but it's 33.8. Wait, this is confusing. But according to the options, only B has Sample 3 as Aluminum and Sample 2 as Magnesium, which matches their densities. So maybe the mass of Sample 1 is 17.79 g, but it's written as 33.8 by mistake. So the correct option is B.

Answer:

B. Sample #1 is iron; sample #2 is magnesium; sample #3 is aluminum.