Question
Malika models the volume of a popcorn box as a right rectangular prism and the box can hold 35 cubic inches of popcorn when it is full. Its length is 22 in and its width is 2, one half2
2
1
in. Find the height of the popcorn box in inches. Round your answer to the nearest tenth if necessary.
Answer
Attempt 1 out of 2
in in
2
1
in. Find the height of the popcorn box in inches. Round your answer to the nearest tenth if necessary.
Answer
Attempt 1 out of 2
in in
Answers
Answered by
GPT-4o mini
To find the height of the popcorn box modeled as a right rectangular prism, we can use the formula for the volume of a rectangular prism:
\[
V = l \times w \times h
\]
where:
- \( V \) is the volume,
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
We are given the following:
- Volume \( V = 35 \) cubic inches,
- Length \( l = 22 \) inches,
- Width \( w = 2.5 \) inches (since one half is 0.5, and \( 2 + 0.5 = 2.5 \)).
Now we can substitute the given values into the volume formula and solve for \( h \):
\[
35 = 22 \times 2.5 \times h
\]
First, calculate \( 22 \times 2.5 \):
\[
22 \times 2.5 = 55
\]
Now we can rewrite the equation:
\[
35 = 55 \times h
\]
To solve for \( h \), divide both sides by 55:
\[
h = \frac{35}{55}
\]
Simplifying that fraction:
\[
h = \frac{7}{11} \approx 0.63636 \text{ inches}
\]
Now rounding to the nearest tenth:
\[
h \approx 0.6 \text{ inches}
\]
Thus, the height of the popcorn box is approximately:
\[
\boxed{0.6} \text{ inches}
\]
\[
V = l \times w \times h
\]
where:
- \( V \) is the volume,
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
We are given the following:
- Volume \( V = 35 \) cubic inches,
- Length \( l = 22 \) inches,
- Width \( w = 2.5 \) inches (since one half is 0.5, and \( 2 + 0.5 = 2.5 \)).
Now we can substitute the given values into the volume formula and solve for \( h \):
\[
35 = 22 \times 2.5 \times h
\]
First, calculate \( 22 \times 2.5 \):
\[
22 \times 2.5 = 55
\]
Now we can rewrite the equation:
\[
35 = 55 \times h
\]
To solve for \( h \), divide both sides by 55:
\[
h = \frac{35}{55}
\]
Simplifying that fraction:
\[
h = \frac{7}{11} \approx 0.63636 \text{ inches}
\]
Now rounding to the nearest tenth:
\[
h \approx 0.6 \text{ inches}
\]
Thus, the height of the popcorn box is approximately:
\[
\boxed{0.6} \text{ inches}
\]
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