Question
A lead sphere has a mass of \( 1.20 \times 10^{4} \mathrm{~g} \), and its volume is \( 1.14 \times 10^{3} \mathrm{~cm}^{3} \). Calculate its density. Round your answer to 3 significant digits.
Ask by French Nguyen. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The sphere's density is 10.5 g/cm³.
Solution
To calculate the density of the lead sphere, use the formula:
\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]
**Given:**
- Mass (\( m \)) = \( 1.20 \times 10^{4} \) g
- Volume (\( V \)) = \( 1.14 \times 10^{3} \) cm³
**Calculation:**
\[
\text{Density} = \frac{1.20 \times 10^{4}\, \text{g}}{1.14 \times 10^{3}\, \text{cm}^3} = \frac{12000\, \text{g}}{1140\, \text{cm}^3} \approx 10.5263\, \text{g/cm}^3
\]
**Rounding to 3 Significant Digits:**
\[
\text{Density} \approx 10.5\, \text{g/cm}^3
\]
**Answer:**
The sphere’s density is 10.5 g cm⁻³ when rounded to three significant digits.
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Simplify this solution The Deep Dive
To calculate the density of the lead sphere, use the formula for density: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \] First, convert the mass to grams and the volume to cubic centimeters: - Mass = \( 1.20 \times 10^{4} \, \text{g} \) - Volume = \( 1.14 \times 10^{3} \, \text{cm}^{3} \) Now, plug in the values: \[ \text{Density} = \frac{1.20 \times 10^{4} \, \text{g}}{1.14 \times 10^{3} \, \text{cm}^{3}} \approx 10.5263 \, \text{g/cm}^3 \] Rounding this to three significant digits, the density of the lead sphere is: \[ \text{Density} \approx 10.5 \, \text{g/cm}^3 \]
