Question
Which method would determine the volume of the prism with dimensions 2 times 2 and one-fourth times 4 shown below?
A prism has a length of 2 and one-fourth, height of 4, and width of 2 inches.
There are 8 one-quarter cubes and 16 unit cubes so (8 times one-fourth) + 16 will give the volume.
There are 8 one-quarter cubes and 8 unit cubes so (8 times one-fourth) + 8 will give the volume.
There are 8 one-quarter cubes and 16 unit cubes so (8 times 4) + 16 will give the volume.
There are 8 one-quarter cubes and 8 unit cubes so (8 times 4) + 8 will give the volume.
A prism has a length of 2 and one-fourth, height of 4, and width of 2 inches.
There are 8 one-quarter cubes and 16 unit cubes so (8 times one-fourth) + 16 will give the volume.
There are 8 one-quarter cubes and 8 unit cubes so (8 times one-fourth) + 8 will give the volume.
There are 8 one-quarter cubes and 16 unit cubes so (8 times 4) + 16 will give the volume.
There are 8 one-quarter cubes and 8 unit cubes so (8 times 4) + 8 will give the volume.
Answers
Answered by
GPT-4o mini
To determine the volume of the prism with dimensions of 2 and one-fourth (which can be written as \(2.25\) or \(\frac{9}{4}\)), height of 4, and width of 2 inches, we would calculate the volume using the formula for the volume of a rectangular prism:
\[
\text{Volume} = \text{Length} \times \text{Height} \times \text{Width}
\]
Substituting the values for the dimensions:
\[
\text{Volume} = \left(2\frac{1}{4}\right) \times 4 \times 2
\]
Converting \(2\frac{1}{4}\) to an improper fraction gives \(\frac{9}{4}\):
\[
\text{Volume} = \frac{9}{4} \times 4 \times 2
\]
Calculating this step by step:
1. \( \frac{9}{4} \times 4 = 9 \)
2. Then multiplying by 2: \( 9 \times 2 = 18 \)
Thus, the volume is \(18\) cubic inches.
Now, regarding the options you provided, let’s analyze them for correct reasoning:
1. **There are 8 one-quarter cubes and 16 unit cubes so (8 times one-fourth) + 16 will give the volume.**
- This option is incorrect because it adds 16 cubes, suggesting the wrong calculation.
2. **There are 8 one-quarter cubes and 8 unit cubes so (8 times one-fourth) + 8 will give the volume.**
- This option is also incorrect since it mistakenly states the number of unit cubes involved (which should be 16, not 8).
3. **There are 8 one-quarter cubes and 16 unit cubes so (8 times 4) + 16 will give the volume.**
- This is incorrect as multiplying 8 by 4 does not relate to the unit volume and also has the wrong context.
4. **There are 8 one-quarter cubes and 8 unit cubes so (8 times 4) + 8 will give the volume.**
- This option is misleading as well in its context and computation.
In conclusion, none of the given options correctly describe the method to find the volume of the prism based on the provided dimensions. The most appropriate way would be to use the formula for volume directly as shown, without involving units cubes or fractional cubes.
\[
\text{Volume} = \text{Length} \times \text{Height} \times \text{Width}
\]
Substituting the values for the dimensions:
\[
\text{Volume} = \left(2\frac{1}{4}\right) \times 4 \times 2
\]
Converting \(2\frac{1}{4}\) to an improper fraction gives \(\frac{9}{4}\):
\[
\text{Volume} = \frac{9}{4} \times 4 \times 2
\]
Calculating this step by step:
1. \( \frac{9}{4} \times 4 = 9 \)
2. Then multiplying by 2: \( 9 \times 2 = 18 \)
Thus, the volume is \(18\) cubic inches.
Now, regarding the options you provided, let’s analyze them for correct reasoning:
1. **There are 8 one-quarter cubes and 16 unit cubes so (8 times one-fourth) + 16 will give the volume.**
- This option is incorrect because it adds 16 cubes, suggesting the wrong calculation.
2. **There are 8 one-quarter cubes and 8 unit cubes so (8 times one-fourth) + 8 will give the volume.**
- This option is also incorrect since it mistakenly states the number of unit cubes involved (which should be 16, not 8).
3. **There are 8 one-quarter cubes and 16 unit cubes so (8 times 4) + 16 will give the volume.**
- This is incorrect as multiplying 8 by 4 does not relate to the unit volume and also has the wrong context.
4. **There are 8 one-quarter cubes and 8 unit cubes so (8 times 4) + 8 will give the volume.**
- This option is misleading as well in its context and computation.
In conclusion, none of the given options correctly describe the method to find the volume of the prism based on the provided dimensions. The most appropriate way would be to use the formula for volume directly as shown, without involving units cubes or fractional cubes.