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:

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

We are given:
- Mass = 1260 grams
- Density = 1.2 g/cm³

First, we can find the volume of the prism using the density formula rearranged to solve for volume:

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

Now, we can use the volume of the rectangular prism formula:

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

Substituting the known values (length = 8 cm, width = 15 cm):

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

Calculating the area of the base:

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

Thus, the equation becomes:

\[
1050 \text{ cm}^3 = 120 \text{ cm}^2 \times \text{height}
\]

To find the height, we divide both sides by \(120 \text{ cm}^2\):

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

Therefore, the height of the prism is:

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