Alejandro buys a ring box that is 2 1/2 in x 3 in x 3 in. He places it in a rectangular prism. What is a possible set of dimensions for the rectangular prism? And how much space in inches cubed will be empty with the ring box inside of
Alejandro buys a ring box that is 2 1/2 in x 3 in x 3 in. He places it in a rectangular prism. What is a possible set of dimensions for the rectangular prism? And how much space in inches cubed will be empty with the ring box inside of
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![### Problem 2
**Alejandro buys a ring box that is 2 1/2 in x 3 in x 3 in. He places it in a rectangular prism. What is a possible set of dimensions for the rectangular prism? And how much space in inches cubed will be empty with the ring box inside of it?**
**Step-by-Step Solution:**
1. **Determine the volume of the ring box:**
- Dimensions of ring box: \( 2 \frac{1}{2} \text{ in} \times 3 \text{ in} \times 3 \text{ in} \)
- Convert \( 2 \frac{1}{2} \text{ in} \) to a decimal: \( 2.5 \text{ in} \)
- Calculate the volume of the ring box:
\[
\text{Volume} = 2.5 \text{ in} \times 3 \text{ in} \times 3 \text{ in} = 22.5 \text{ cubic inches}
\]
2. **Determine possible dimensions of the rectangular prism:**
- Possible dimensions for the rectangular prism should be greater than or equal to the dimensions of the ring box.
- Example set of dimensions: \( 4 \text{ in} \times 4 \text{ in} \times 4 \text{ in} \)
- Calculate the volume of the rectangular prism:
\[
\text{Volume} = 4 \text{ in} \times 4 \text{ in} \times 4 \text{ in} = 64 \text{ cubic inches}
\]
3. **Calculate the empty space in the rectangular prism:**
- Subtract the volume of the ring box from the volume of the rectangular prism:
\[
\text{Empty space} = 64 \text{ cubic inches} - 22.5 \text{ cubic inches} = 41.5 \text{ cubic inches}
\]
**Conclusion:**
A possible set of dimensions for the rectangular prism that can contain Alejandro’s ring box could be \( 4 \text{ in} \times 4 \text{ in} \times 4 \text{ in} \). The empty space in the rectangular prism with the ring box inside of it would be \( 41](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F72a25c37-27e2-4a85-ad3d-3261d938835f%2F3a1e234b-73cd-4232-b05e-dbd2643e5b0f%2Fcv5afwe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 2
**Alejandro buys a ring box that is 2 1/2 in x 3 in x 3 in. He places it in a rectangular prism. What is a possible set of dimensions for the rectangular prism? And how much space in inches cubed will be empty with the ring box inside of it?**
**Step-by-Step Solution:**
1. **Determine the volume of the ring box:**
- Dimensions of ring box: \( 2 \frac{1}{2} \text{ in} \times 3 \text{ in} \times 3 \text{ in} \)
- Convert \( 2 \frac{1}{2} \text{ in} \) to a decimal: \( 2.5 \text{ in} \)
- Calculate the volume of the ring box:
\[
\text{Volume} = 2.5 \text{ in} \times 3 \text{ in} \times 3 \text{ in} = 22.5 \text{ cubic inches}
\]
2. **Determine possible dimensions of the rectangular prism:**
- Possible dimensions for the rectangular prism should be greater than or equal to the dimensions of the ring box.
- Example set of dimensions: \( 4 \text{ in} \times 4 \text{ in} \times 4 \text{ in} \)
- Calculate the volume of the rectangular prism:
\[
\text{Volume} = 4 \text{ in} \times 4 \text{ in} \times 4 \text{ in} = 64 \text{ cubic inches}
\]
3. **Calculate the empty space in the rectangular prism:**
- Subtract the volume of the ring box from the volume of the rectangular prism:
\[
\text{Empty space} = 64 \text{ cubic inches} - 22.5 \text{ cubic inches} = 41.5 \text{ cubic inches}
\]
**Conclusion:**
A possible set of dimensions for the rectangular prism that can contain Alejandro’s ring box could be \( 4 \text{ in} \times 4 \text{ in} \times 4 \text{ in} \). The empty space in the rectangular prism with the ring box inside of it would be \( 41
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