Question

A rectangular prism with a length of 10 cm, width of 8 cm, and height of 16 cm has the mass of 1,248 grams.

Find the volume of the prism.

Find the density of the prism.

Do not round.

(2 points)
Volume =
cm3
Density =
g/cm3

Answer 1

To find the volume and the density of the rectangular prism, we can use the following formulas:

1. **Volume of a rectangular prism**:
\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]

2. **Density**:
\[
\text{Density} = \frac{\text{mass}}{\text{volume}}
\]

### Step 1: Calculate the volume

Using the dimensions provided:
- Length = 10 cm
- Width = 8 cm
- Height = 16 cm

Calculating the volume:
\[
\text{Volume} = 10 \, \text{cm} \times 8 \, \text{cm} \times 16 \, \text{cm} = 1280 \, \text{cm}^3
\]

### Step 2: Calculate the density

Given the mass of the prism is 1,248 grams, we can find the density using the formula:

\[
\text{Density} = \frac{\text{mass}}{\text{volume}} = \frac{1248 \, \text{g}}{1280 \, \text{cm}^3}
\]

Calculating the density:
\[
\text{Density} = 0.975 \, \text{g/cm}^3
\]

### Final Answers
- Volume = **1280 cm³**
- Density = **0.975 g/cm³**