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 that relates mass, density, and volume:

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

From this, we can rearrange the formula to find the volume:

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

Given the mass is 1,260 grams and the density is 1.2 g/cm³, we can calculate the volume:

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

Next, we also know the volume of a rectangular prism is calculated as:

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

Substituting the known values into the volume formula:

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

Calculating \(8 \times 15\):

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

Now, to find the height, we divide both sides by 120:

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

Calculating the division:

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

Thus, the height of the prism is **8.75 cm**.