Question
A storage container that is in the shape of a rectangular prism has a volume of 60 cubic foot what could be the dimensions of the container if one dimension is 3 ft and all dimensions are whole units A 3 ft by 4 ft by 5 ft B 3 ft by 3 ft by 5 ft C 3 ft x 5 ft by 6 ft D 3 ft by 2 ft by 10 ft E 3 ft by 2 ft x 15 ft
Answers
GPT-4o mini
To determine the potential dimensions of a rectangular prism (storage container) given that one dimension is 3 ft and the volume is 60 cubic feet, we can use the formula for the volume of a rectangular prism:
\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]
Given that one of the dimensions is 3 ft, we can express the volume as:
\[
60 = 3 \times \text{width} \times \text{height}
\]
We can simplify this to find the product of the other two dimensions:
\[
\text{width} \times \text{height} = \frac{60}{3} = 20
\]
Now we need to find pairs of whole numbers (width and height) that multiply to 20.
The pairs of whole numbers that yield a product of 20 are:
- \(1 \times 20\)
- \(2 \times 10\)
- \(4 \times 5\)
Now, let's evaluate the options provided:
A. \(3 \, \text{ft} \times 4 \, \text{ft} \times 5 \, \text{ft}\)
\[
3 \times 4 \times 5 = 60 \, \text{cubic ft} \quad \text{(Valid)}
\]
B. \(3 \, \text{ft} \times 3 \, \text{ft} \times 5 \, \text{ft}\)
\[
3 \times 3 \times 5 = 45 \, \text{cubic ft} \quad \text{(Invalid)}
\]
C. \(3 \, \text{ft} \times 5 \, \text{ft} \times 6 \, \text{ft}\)
\[
3 \times 5 \times 6 = 90 \, \text{cubic ft} \quad \text{(Invalid)}
\]
D. \(3 \, \text{ft} \times 2 \, \text{ft} \times 10 \, \text{ft}\)
\[
3 \times 2 \times 10 = 60 \, \text{cubic ft} \quad \text{(Valid)}
\]
E. \(3 \, \text{ft} \times 2 \, \text{ft} \times 15 \, \text{ft}\)
\[
3 \times 2 \times 15 = 90 \, \text{cubic ft} \quad \text{(Invalid)}
\]
Thus, the valid options are A and D:
- A. \(3 \, \text{ft} \times 4 \, \text{ft} \times 5 \, \text{ft}\)
- D. \(3 \, \text{ft} \times 2 \, \text{ft} \times 10 \, \text{ft}\)
Therefore, the dimensions of the container could be either A or D.
\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]
Given that one of the dimensions is 3 ft, we can express the volume as:
\[
60 = 3 \times \text{width} \times \text{height}
\]
We can simplify this to find the product of the other two dimensions:
\[
\text{width} \times \text{height} = \frac{60}{3} = 20
\]
Now we need to find pairs of whole numbers (width and height) that multiply to 20.
The pairs of whole numbers that yield a product of 20 are:
- \(1 \times 20\)
- \(2 \times 10\)
- \(4 \times 5\)
Now, let's evaluate the options provided:
A. \(3 \, \text{ft} \times 4 \, \text{ft} \times 5 \, \text{ft}\)
\[
3 \times 4 \times 5 = 60 \, \text{cubic ft} \quad \text{(Valid)}
\]
B. \(3 \, \text{ft} \times 3 \, \text{ft} \times 5 \, \text{ft}\)
\[
3 \times 3 \times 5 = 45 \, \text{cubic ft} \quad \text{(Invalid)}
\]
C. \(3 \, \text{ft} \times 5 \, \text{ft} \times 6 \, \text{ft}\)
\[
3 \times 5 \times 6 = 90 \, \text{cubic ft} \quad \text{(Invalid)}
\]
D. \(3 \, \text{ft} \times 2 \, \text{ft} \times 10 \, \text{ft}\)
\[
3 \times 2 \times 10 = 60 \, \text{cubic ft} \quad \text{(Valid)}
\]
E. \(3 \, \text{ft} \times 2 \, \text{ft} \times 15 \, \text{ft}\)
\[
3 \times 2 \times 15 = 90 \, \text{cubic ft} \quad \text{(Invalid)}
\]
Thus, the valid options are A and D:
- A. \(3 \, \text{ft} \times 4 \, \text{ft} \times 5 \, \text{ft}\)
- D. \(3 \, \text{ft} \times 2 \, \text{ft} \times 10 \, \text{ft}\)
Therefore, the dimensions of the container could be either A or D.