Question

refer to the table of densities at the right to answer the following questions.
substance density (g/ml)
aluminum 2.70
titanium 4.54
zinc 7.13
tin 7.31
iron 7.87
nickel 8.90
copper 8.96
silver 10.50
lead 11.35
mercury 13.55
gold 19.30

1. sketch a graph of mass vs. volume for titanium, copper and mercury.

1. you made some cubes out of each metal in the table that each measures 2.00 cm on every side. (all except mercury – why can’t you make a cube of mercury?)

a. what is the volume of each cube in cm³? in ml? (show your thinking)

b. find the mass of these metal cubes: (show your work below)
lead cube 90.8g
nickel cube 71.2g
zinc cube 57.04g

Explanation:

6a.

Step1: Recall volume of cube formula

The formula for the volume \( V \) of a cube is \( V = s^3 \), where \( s \) is the length of a side.

Step2: Substitute side length

Given \( s = 2.00 \, \text{cm} \), so \( V=(2.00\,\text{cm})^3 = 8.00\,\text{cm}^3 \).

Step3: Relate \( \text{cm}^3 \) and \( \text{mL} \)

We know that \( 1\,\text{cm}^3 = 1\,\text{mL} \), so \( 8.00\,\text{cm}^3 = 8.00\,\text{mL} \).

Step1: Recall density formula

Density \(
ho=\frac{m}{V} \), so \( m =
ho\times V \).

Step2: Get density of lead

From the table, density of lead \(
ho = 11.35\,\text{g/mL} \), volume \( V = 8.00\,\text{mL} \).

Step3: Calculate mass

\( m=
ho\times V = 11.35\,\text{g/mL}\times8.00\,\text{mL}=90.8\,\text{g} \) (matches the given value).

Nickel cube:

Step1: Density of nickel

From table, \(
ho = 8.90\,\text{g/mL} \), \( V = 8.00\,\text{mL} \).

Step2: Calculate mass

\( m=
ho\times V = 8.90\,\text{g/mL}\times8.00\,\text{mL}=71.2\,\text{g} \) (matches the given value).

Zinc cube:

Answer:

The volume of each cube is \( 8.00\,\text{cm}^3 \) (or \( 8.00\,\text{mL} \)).

6b. (Let's verify the given masses or calculate if needed, here we can show the calculation for one to check)

Take lead cube: