Question
Question
A storage container that is in the shape of a rectangular prism has a volume of 60 cubic feet. What could be the dimensions of the container if one dimension is 3 feet and all dimensions are whole units? Select all that apply.
(1 point)
Responses
3 feet by 4 feet by 5 feet
3 feet by 4 feet by 5 feet
3 feet by 3 feet by 5 feet
3 feet by 3 feet by 5 feet
3 feet by 5 feet by 6 feet
3 feet by 5 feet by 6 feet
3 feet by 2 feet by 10 feet
3 feet by 2 feet by 10 feet
3 feet by 2 feet by 15 feet
A storage container that is in the shape of a rectangular prism has a volume of 60 cubic feet. What could be the dimensions of the container if one dimension is 3 feet and all dimensions are whole units? Select all that apply.
(1 point)
Responses
3 feet by 4 feet by 5 feet
3 feet by 4 feet by 5 feet
3 feet by 3 feet by 5 feet
3 feet by 3 feet by 5 feet
3 feet by 5 feet by 6 feet
3 feet by 5 feet by 6 feet
3 feet by 2 feet by 10 feet
3 feet by 2 feet by 10 feet
3 feet by 2 feet by 15 feet
Answers
GPT-4o mini
To find the possible dimensions of the rectangular prism with a volume of 60 cubic feet and one dimension equal to 3 feet, we can use the formula for the volume of a rectangular prism:
\[
Volume = length \times width \times height
\]
Given that one dimension is 3 feet, we can represent the volume as:
\[
60 = 3 \times width \times height
\]
Dividing both sides by 3 gives:
\[
width \times height = 20
\]
Now we need to find pairs of whole numbers (width, height) that multiply to 20. The pairs are:
1. \(1 \times 20\)
2. \(2 \times 10\)
3. \(4 \times 5\)
4. \(5 \times 4\)
5. \(10 \times 2\)
6. \(20 \times 1\)
Next, we can list the potential dimensions of the container using the identified pairs, including the given dimension of 3 feet:
- 3 feet by 1 foot by 20 feet
- 3 feet by 2 feet by 10 feet
- 3 feet by 4 feet by 5 feet
- 3 feet by 5 feet by 4 feet
- 3 feet by 10 feet by 2 feet
- 3 feet by 20 feet by 1 foot
Now, let's check the given responses:
1. **3 feet by 4 feet by 5 feet** - This is correct since \(3 \times 4 \times 5 = 60\).
2. **3 feet by 3 feet by 5 feet** - This is incorrect since \(3 \times 3 \times 5 = 45\).
3. **3 feet by 5 feet by 6 feet** - This is incorrect since \(3 \times 5 \times 6 = 90\).
4. **3 feet by 2 feet by 10 feet** - This is correct since \(3 \times 2 \times 10 = 60\).
5. **3 feet by 2 feet by 15 feet** - This is incorrect since \(3 \times 2 \times 15 = 90\).
The responses that apply are:
- 3 feet by 4 feet by 5 feet
- 3 feet by 2 feet by 10 feet
\[
Volume = length \times width \times height
\]
Given that one dimension is 3 feet, we can represent the volume as:
\[
60 = 3 \times width \times height
\]
Dividing both sides by 3 gives:
\[
width \times height = 20
\]
Now we need to find pairs of whole numbers (width, height) that multiply to 20. The pairs are:
1. \(1 \times 20\)
2. \(2 \times 10\)
3. \(4 \times 5\)
4. \(5 \times 4\)
5. \(10 \times 2\)
6. \(20 \times 1\)
Next, we can list the potential dimensions of the container using the identified pairs, including the given dimension of 3 feet:
- 3 feet by 1 foot by 20 feet
- 3 feet by 2 feet by 10 feet
- 3 feet by 4 feet by 5 feet
- 3 feet by 5 feet by 4 feet
- 3 feet by 10 feet by 2 feet
- 3 feet by 20 feet by 1 foot
Now, let's check the given responses:
1. **3 feet by 4 feet by 5 feet** - This is correct since \(3 \times 4 \times 5 = 60\).
2. **3 feet by 3 feet by 5 feet** - This is incorrect since \(3 \times 3 \times 5 = 45\).
3. **3 feet by 5 feet by 6 feet** - This is incorrect since \(3 \times 5 \times 6 = 90\).
4. **3 feet by 2 feet by 10 feet** - This is correct since \(3 \times 2 \times 10 = 60\).
5. **3 feet by 2 feet by 15 feet** - This is incorrect since \(3 \times 2 \times 15 = 90\).
The responses that apply are:
- 3 feet by 4 feet by 5 feet
- 3 feet by 2 feet by 10 feet