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 density of the prism.

Answer 1

To find the density of the rectangular prism, we can use the formula for density:

\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]

First, we need to calculate the volume of the rectangular prism. The volume \( V \) of a rectangular prism can be calculated using the formula:

\[
V = \text{Length} \times \text{Width} \times \text{Height}
\]

Given:
- Length = 10 cm
- Width = 8 cm
- Height = 16 cm

Substituting these values into the volume formula:

\[
V = 10 \, \text{cm} \times 8 \, \text{cm} \times 16 \, \text{cm}
\]

Calculating the volume:

\[
V = 10 \times 8 = 80 \, \text{cm}^2
\]
\[
V = 80 \times 16 = 1280 \, \text{cm}^3
\]

Now we have the volume of the prism, which is \( 1280 \, \text{cm}^3 \).

Next, we use the mass of the prism, which is given as \( 1248 \, \text{g} \), to calculate the density:

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

Now, performing the division:

\[
\text{Density} = 0.975 \, \text{g/cm}^3
\]

Thus, the density of the rectangular prism is:

\[
\boxed{0.975 \, \text{g/cm}^3}
\]