Question

A rectangular prism with a length of 8 centimeters, width of 15 centimeters, and an unknown height has a mass of 1,260 grams and a density of 1.2 g/cm3
. Find the height of the prism.(1 point)
cm

Answer 1

To find the height of the rectangular prism, we can start by using the formula for density:

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

We can rearrange this formula to find the volume:

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

Substituting the given values:

\[
\text{Volume} = \frac{1260 \, \text{grams}}{1.2 \, \text{g/cm}^3} = 1050 \, \text{cm}^3
\]

Now, the volume \( V \) of a rectangular prism is also given by the formula:

\[
V = \text{length} \times \text{width} \times \text{height}
\]

Substituting the known values:

\[
1050 \, \text{cm}^3 = 8 \, \text{cm} \times 15 \, \text{cm} \times h
\]

Calculating the length times width:

\[
1050 = 120 \, \text{cm}^2 \times h
\]

Now, to solve for \( h \), we can divide both sides by 120:

\[
h = \frac{1050 \, \text{cm}^3}{120 \, \text{cm}^2} = 8.75 \, \text{cm}
\]

Thus, the height of the prism is:

\[
\boxed{8.75} \, \text{cm}
\]