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/cm^3. Find the height of the prism.

__ cm

Answer 1

To find the height of the rectangular prism, we can use the relationship between mass, density, and volume defined by the formula:

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

From this, we can derive the volume of the prism using the rearranged formula:

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

Given:

- Mass = 1260 grams
- Density = 1.2 g/cm³

Now, we can calculate the volume:

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

Next, we can find the height of the prism. The volume \( V \) of a rectangular prism is given by the formula:

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

Substituting the known values \( V = 1050 \text{ cm}^3 \), length = 8 cm, and width = 15 cm:

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

Calculating the product of length and width:

\[
8 \times 15 = 120
\]

Now we can rewrite the equation:

\[
1050 = 120 \times \text{height}
\]

To find the height, we divide both sides by 120:

\[
\text{height} = \frac{1050}{120}
\]

Calculating the height:

\[
\text{height} = 8.75 \text{ cm}
\]

Thus, the height of the prism is:

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