Question
A rectangular prism made of inch cubes is shown.
The rectangle prism has 3 layers. Each layer has 6 rows of 5 unit cubes.
Which statement about the rectangular prism is true?
A.
The rectangular prism is made up of 90 unit cubes. The volume can be found by multiplying 18 square inches by 6 inches.
B.
The rectangular prism is made up of 90 unit cubes. The volume can be found by multiplying 30 square inches by 3 inches.
C.
The rectangular prism is made up of 108 unit cubes. The volume can be found by multiplying 15 square inches by 6 inches.
D.
The rectangular prism is made up of 108 unit cubes. The volume can be found by multiplying 36 square inches by 3 inches.
The rectangle prism has 3 layers. Each layer has 6 rows of 5 unit cubes.
Which statement about the rectangular prism is true?
A.
The rectangular prism is made up of 90 unit cubes. The volume can be found by multiplying 18 square inches by 6 inches.
B.
The rectangular prism is made up of 90 unit cubes. The volume can be found by multiplying 30 square inches by 3 inches.
C.
The rectangular prism is made up of 108 unit cubes. The volume can be found by multiplying 15 square inches by 6 inches.
D.
The rectangular prism is made up of 108 unit cubes. The volume can be found by multiplying 36 square inches by 3 inches.
Answers
GPT-4o mini
To find the volume of the rectangular prism, we need to calculate the total number of unit cubes and relate it to the formula for volume.
1. The prism has **3 layers**.
2. Each layer has **6 rows** and each row contains **5 unit cubes**.
First, we calculate the number of unit cubes in one layer:
- Number of unit cubes in one layer = Number of rows × Number of cubes per row = 6 × 5 = 30 unit cubes.
Now, to find the total number of unit cubes in the prism:
- Total unit cubes = Number of layers × Number of unit cubes per layer = 3 × 30 = 90 unit cubes.
Next, we need to verify the statements concerning the volume:
- The volume of the prism can be formulated as the number of cubes (which is 90) and defined in terms of square inches multiplied by the height in inches.
Now let's evaluate the options:
A.
- It states 90 unit cubes. For the volume, it mentions 18 square inches × 6 inches; this gives 108 cubic inches. Thus, this statement is **false**.
B.
- It states 90 unit cubes and talks about multiplying 30 square inches by 3 inches. This gives 90 cubic inches. Thus, this statement is **true**.
C.
- It states 108 unit cubes and volume found by multiplying 15 square inches by 6 inches. This gives 90 cubic inches, and since the cube count is also incorrect, this is **false**.
D.
- It states 108 unit cubes and multiplying 36 square inches by 3 inches, resulting in 108 cubic inches, but again, the cube count is incorrect, making this statement **false**.
Only option **B** correctly states the number of unit cubes (90) and uses a volume formula that is appropriate given the count of cubes (30 square inches x 3 inches). Hence, the correct answer is:
**B.** The rectangular prism is made up of 90 unit cubes. The volume can be found by multiplying 30 square inches by 3 inches.
1. The prism has **3 layers**.
2. Each layer has **6 rows** and each row contains **5 unit cubes**.
First, we calculate the number of unit cubes in one layer:
- Number of unit cubes in one layer = Number of rows × Number of cubes per row = 6 × 5 = 30 unit cubes.
Now, to find the total number of unit cubes in the prism:
- Total unit cubes = Number of layers × Number of unit cubes per layer = 3 × 30 = 90 unit cubes.
Next, we need to verify the statements concerning the volume:
- The volume of the prism can be formulated as the number of cubes (which is 90) and defined in terms of square inches multiplied by the height in inches.
Now let's evaluate the options:
A.
- It states 90 unit cubes. For the volume, it mentions 18 square inches × 6 inches; this gives 108 cubic inches. Thus, this statement is **false**.
B.
- It states 90 unit cubes and talks about multiplying 30 square inches by 3 inches. This gives 90 cubic inches. Thus, this statement is **true**.
C.
- It states 108 unit cubes and volume found by multiplying 15 square inches by 6 inches. This gives 90 cubic inches, and since the cube count is also incorrect, this is **false**.
D.
- It states 108 unit cubes and multiplying 36 square inches by 3 inches, resulting in 108 cubic inches, but again, the cube count is incorrect, making this statement **false**.
Only option **B** correctly states the number of unit cubes (90) and uses a volume formula that is appropriate given the count of cubes (30 square inches x 3 inches). Hence, the correct answer is:
**B.** The rectangular prism is made up of 90 unit cubes. The volume can be found by multiplying 30 square inches by 3 inches.