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 use the formula for density:

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

First, we rearrange the formula to find the volume:

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

We know the mass is 1,260 grams and the density is 1.2 g/cm³:

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

Next, we can find the volume of the rectangular prism using the formula for the volume of a rectangular prism:

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

We know the length (8 cm) and the width (15 cm), so we can express the volume as:

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

Now, calculating the area of the base:

\[
8 \times 15 = 120 \, \text{cm}^2
\]

Now we can find the height \( h \):

\[
1050 = 120 \times h
\]

Solving for \( h \):

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

Thus, the height of the prism is:

\[
\boxed{8.75}
\] cm.