Question 2 of 3
Sylvie made the solid figures shown using unit cubes.
Which statement about these models is true?
Model A has length as 6 unit cubes, height as 2 unit cubes and width as 3 unit cubes. Model B has length as 10 unit cubes, height as 2 unit cubes and width as 2 unit cubes.
A.
The volume of Model A is 10 cubic units less than the volume of Model B.
B.
The volume of Model B is 4 cubic units greater than the volume of Model A.
C.
The volume of Model A and Model B combined is 54 cubic units.
D.
Model A and Model B have the same volume.
The answer is D. Model A and Model B have the same volume.
To find the volume of a rectangular prism, you multiply its length, width, and height.
For Model A, length x width x height = 6 x 3 x 2 = 36 cubic units.
For Model B, length x width x height = 10 x 2 x 2 = 40 cubic units.
Therefore, Model A and Model B have different volumes, and A is not 10 cubic units less or B is not 4 cubic units greater. The only option that is true is that they have the same volume, which is the answer D.
To determine the correct statement about the models, we need to calculate their respective volumes and compare them.
The volume of a solid figure is calculated by multiplying its length, height, and width. For Model A, the length is 6 unit cubes, the height is 2 unit cubes, and the width is 3 unit cubes. Thus, the volume of Model A can be calculated as 6 * 2 * 3 = 36 cubic units.
For Model B, the length is 10 unit cubes, the height is 2 unit cubes, and the width is 2 unit cubes. Therefore, the volume of Model B can be calculated as 10 * 2 * 2 = 40 cubic units.
Now that we have calculated the volumes of both models, we can evaluate the given statements:
A. The volume of Model A is 10 cubic units less than the volume of Model B: Since the volume of Model B (40 cubic units) is greater than the volume of Model A (36 cubic units), this statement is false.
B. The volume of Model B is 4 cubic units greater than the volume of Model A: Since the volume of Model B is indeed greater by 4 cubic units (40 - 36 = 4), this statement is true.
C. The volume of Model A and Model B combined is 54 cubic units: The combined volume of Model A (36 cubic units) and Model B (40 cubic units) is 36 + 40 = 76 cubic units. Therefore, this statement is false.
D. Model A and Model B have the same volume: Since their volumes are different (36 cubic units for Model A and 40 cubic units for Model B), this statement is false.
Based on the calculations above, the correct statement is B. The volume of Model B is 4 cubic units greater than the volume of Model A.
To find the volume of a solid figure, we need to multiply its length, height, and width.
For Model A, the length is 6 unit cubes, the height is 2 unit cubes, and the width is 3 unit cubes. Therefore, the volume of Model A is 6 x 2 x 3 = 36 cubic units.
For Model B, the length is 10 unit cubes, the height is 2 unit cubes, and the width is 2 unit cubes. Therefore, the volume of Model B is 10 x 2 x 2 = 40 cubic units.
Since the volume of Model A is 36 cubic units and the volume of Model B is 40 cubic units, we can see that the statement "The volume of Model B is 4 cubic units greater than the volume of Model A" (option B) is true.