Question

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

__ g/cm^3

Answer 1

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

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

First, we need to calculate the volume of the prism using the formula for the volume of a rectangular prism:

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

Given the dimensions of the prism:

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

Now, substituting the values into the volume formula:

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

Calculating this:

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

Now that we have the volume, we can substitute the mass of the prism into the density formula. The mass is given as 1,248 grams.

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

Now, calculating the density:

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

Therefore, the density of the prism is

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