Determine the mass of the pennies and use your labkit ruler to determine their volume. Use those values to calculate density.
| Object: | Mass (g) | Diameter (cm) | Radius (½ diameter) | Height (cm) | Volume (cm³) | Density (g/cm³) |
|---|---|---|---|---|---|---|
| 5 pennies | 12.48 | 1.90 | 0.95 | 0.5 | 38 cm³ | 32 g/cm³ |
(Volume of this stack of pennies is the volume of a cylinder, V = h × π × radius²)
Answer (1)
To determine the density of the stack of 5 pennies, you need to calculate their volume and then use the density formula. Density is defined as mass divided by volume.
Let's break it down step-by-step:
Mass Calculation : The mass of the 5 pennies is already given as 12.48 grams.
Volume Calculation : The volume of the stack of pennies is calculated as the volume of a cylinder. The formula for the volume of a cylinder, V , is:
V = h × π × ( r a d i u s ) 2
Given:
Diameter of one penny: 1.90 cm
Radius: 2 1.90 = 0.95 cm
Height of the stack (assuming it is given as 0.5 cm per penny and then multiplied by 5 since there are 5 pennies): 2.5 cm
Using these values in the formula:
V = 2.5 × π × ( 0.95 ) 2
V ≈ 2.5 × 3.14159 × 0.9025
V ≈ 2.5 × 2.835 ≈ 7.0875 cm 3
Density Calculation : The density ρ is determined as follows:
ρ = volume mass
ρ = 7.0875 cm 3 12.48 g
ρ ≈ 1.76 g/cm 3
The calculated density of the stack of 5 pennies is approximately 1.76 g/cm³. This value can help understand the material composition of the pennies based on known densities of metals.
