Problem 1: Platinum Bar
#### Given:
- Length of the platinum bar: \( 5.0 \, \text{cm} \)
- Width of the platinum bar: \( 4.0 \, \text{cm} \)
- Thickness of the platinum bar: \( 1.5 \, \text{cm} \)
- Mass of the platinum bar: \( 700.0 \, \text{g} \)
#### Part (a): Calculate the volume of the platinum bar.
The volume \( V \) of a rectangular prism (or bar) is given by the formula:
\[
V = \text{length} \times \text{width} \times \text{thickness}
\]
Substitute the given values:
\[
V = 5.0 \, \text{cm} \times 4.0 \, \text{cm} \times 1.5 \, \text{cm}
\]
Calculate step-by-step:
\[
V = 5.0 \times 4.0 = 20.0 \, \text{cm}^2
\]
\[
V = 20.0 \times 1.5 = 30.0 \, \text{cm}^3
\]
Thus, the volume of the platinum bar is:
\[
\boxed{30.0 \, \text{cm}^3}
\]
#### Part (b): Calculate the density of the platinum bar.
The density \( d \) is given by the formula:
\[
d = \frac{\text{mass}}{\text{volume}}
\]
Substitute the given mass and the calculated volume:
\[
d = \frac{700.0 \, \text{g}}{30.0 \, \text{cm}^3}
\]
Perform the division:
\[
d = 23.3333 \, \text{g/cm}^3
\]
Rounding to two decimal places (as is common in such calculations):
\[
d \approx 23.33 \, \text{g/cm}^3
\]
Thus, the density of the platinum bar is:
\[
\boxed{23.33 \, \text{g/cm}^3}
\]
---
Problem 2: Lead Cylinder
#### Given:
- Mass of the lead cylinder: \( 540 \, \text{g} \)
- Density of the lead cylinder: \( 2.70 \, \text{g/cm}^3 \)
#### Task: Calculate the volume of the lead cylinder.
The volume \( V \) can be calculated using the rearranged density formula:
\[
V = \frac{\text{mass}}{\text{density}}
\]
Substitute the given values:
\[
V = \frac{540 \, \text{g}}{2.70 \, \text{g/cm}^3}
\]
Perform the division:
\[
V = 200 \, \text{cm}^3
\]
Thus, the volume of the lead cylinder is:
\[
\boxed{200 \, \text{cm}^3}
\]
---
Final Answers:
1. (a) Volume of the platinum bar: \(\boxed{30.0 \, \text{cm}^3}\)
(b) Density of the platinum bar: \(\boxed{23.33 \, \text{g/cm}^3}\)
2. Volume of the lead cylinder: \(\boxed{200 \, \text{cm}^3}\)
Parent Tip: Review the logic above to help your child master the concept of density practice problem worksheet.
