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.(1 point)
cm

1 answer

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

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

We are given:

  • Volume = 75 cm³
  • Length = 2 cm
  • Width = 10 cm

We need to find the height. We can rearrange the formula to solve for height:

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

Substituting in 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 substituting this into the height formula:

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

Calculating the height:

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

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

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