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
Remaining Attempts : 3
? Write your answer in decimal form. Express your answer as a decimal rounded to the nearest hundredth.(1 point)
cm
Remaining Attempts : 3
Answers
GPT-4o mini
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 know the volume (75 cm³), length (2 cm), and width (10 cm). We need to find the height (h). The formula can be rearranged to:
\[
\text{Height} = \frac{\text{Volume}}{\text{Length} \times \text{Width}}
\]
Substituting in 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, we can find the height:
\[
\text{Height} = \frac{75 \, \text{cm}^3}{20 \, \text{cm}^2} = 3.75 \, \text{cm}
\]
Thus, the height of the rectangular prism is:
\[
\boxed{3.75} \, \text{cm}
\]
\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]
We know the volume (75 cm³), length (2 cm), and width (10 cm). We need to find the height (h). The formula can be rearranged to:
\[
\text{Height} = \frac{\text{Volume}}{\text{Length} \times \text{Width}}
\]
Substituting in 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, we can find the height:
\[
\text{Height} = \frac{75 \, \text{cm}^3}{20 \, \text{cm}^2} = 3.75 \, \text{cm}
\]
Thus, the height of the rectangular prism is:
\[
\boxed{3.75} \, \text{cm}
\]