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 cm^3
? Write your answer in decimal form. Express your answer as a decimal rounded to the nearest hundredth.(1 point)
cm

Answer 1

To find the height of a right rectangular prism, you can use the formula for the volume of a rectangular prism:

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

Given the volume (75 cm³), length (2 cm), and width (10 cm), we can rearrange the formula to solve for height:

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

Substituting the 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, divide the volume by the area of the base:

\[
\text{height} = \frac{75 \, \text{cm}^3}{20 \, \text{cm}^2} = 3.75 \, \text{cm}
\]

Thus, the height of the right rectangular prism, rounded to the nearest hundredth, is:

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