Question

What is the height of a right rectangular prism with a length of 2 cm, a width of 10 cm, and a volume of 75 cm3
? Write your answer in decimal form. Express your answer as a decimal rounded to the nearest hundredth.

Answer 1

The volume \( V \) of a right rectangular prism can be calculated using the formula:

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

Given:
- Volume \( V = 75 \, \text{cm}^3 \)
- Length = 2 cm
- Width = 10 cm

We can rearrange the formula to solve for height:

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

Substituting the known values:

\[
\text{height} = \frac{75 \, \text{cm}^3}{2 \, \text{cm} \times 10 \, \text{cm}}
\]

Calculating the denominator:

\[
2 \, \text{cm} \times 10 \, \text{cm} = 20 \, \text{cm}^2
\]

Now substituting back into the equation for height:

\[
\text{height} = \frac{75}{20}
\]

Calculating the height:

\[
\text{height} = 3.75 \, \text{cm}
\]

Thus, the height of the right rectangular prism is

\[
\boxed{3.75} \, \text{cm}
\]