Question
A rectangular prism measures 4.53 cm long, 3.455 cm wide, and 4.14 cm tall. It has a mass of 52.70 g . What is the density of this object?
Ask by Frazier Willis. in the United States
Jan 29,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The density of the object is approximately **0.813 g cm⁻³**.
Solution
To determine the density of the rectangular prism, we'll use the formula:
\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]
**Given:**
- Length (L) = 4.53 cm
- Width (W) = 3.455 cm
- Height (H) = 4.14 cm
- Mass (m) = 52.70 g
**Step 1: Calculate the Volume**
The volume \( V \) of a rectangular prism is calculated as:
\[
V = L \times W \times H
\]
\[
V = 4.53 \, \text{cm} \times 3.455 \, \text{cm} \times 4.14 \, \text{cm}
\]
\[
V \approx 4.53 \times 3.455 = 15.65115 \, \text{cm}^2
\]
\[
V \approx 15.65115 \times 4.14 = 64.7958 \, \text{cm}^3
\]
**Step 2: Calculate the Density**
\[
\text{Density} = \frac{52.70 \, \text{g}}{64.7958 \, \text{cm}^3} \approx 0.813 \, \text{g/cm}^3
\]
**Final Answer:**
The density of the object is approximately **0.813 g cm⁻³**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find the density of the rectangular prism, you can use the formula for density: Density = Mass / Volume. First, calculate the volume of the prism by multiplying its length, width, and height: Volume = 4.53 cm × 3.455 cm × 4.14 cm ≈ 62.4206 cm³. Now, divide the mass (52.70 g) by the volume (62.4206 cm³): Density ≈ 52.70 g / 62.4206 cm³ ≈ 0.844 g/cm³. So, the density of the object is approximately 0.844 g/cm³. This means the object is less dense than water (1.0 g/cm³), so it would float if placed in water!
