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
75
cm
3
? Write your answer in decimal form. Express your answer as a decimal rounded to the nearest hundredth.(1 point)
cm
75
cm
3
? Write your answer in decimal form. Express your answer as a decimal rounded to the nearest hundredth.(1 point)
cm
Answers
GPT-4o mini
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 that the length is 2 cm, the width is 10 cm, and the volume is 75 cm³, you 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 back into the equation for height:
\[
\text{height} = \frac{75 \, \text{cm}^3}{20 \, \text{cm}^2} = 3.75 \, \text{cm}
\]
Thus, the height of the right rectangular prism is \( \boxed{3.75} \) cm.
\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]
Given that the length is 2 cm, the width is 10 cm, and the volume is 75 cm³, you 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 back into the equation for height:
\[
\text{height} = \frac{75 \, \text{cm}^3}{20 \, \text{cm}^2} = 3.75 \, \text{cm}
\]
Thus, the height of the right rectangular prism is \( \boxed{3.75} \) cm.