use the unit given. find the volume.
1.
each cube = 1 cu cm
volume = 105 cu cm
2.
8 in.
2 in.
3 in.
each cube = 1 cu in.
volume = cu
3.
7 ft
4 ft
2 ft
each cube = 1 cu ft
volume = cu
4.
5 cm
5 cm
5 cm
each cube = 1 cu cm
volume = cu

compare the volumes. write <, >, or =

5 ft
3 ft
4 ft
each cube = 1 cu ft
cu ft __ cu ft
6 ft
5 ft
2 ft
each cube = 1 cu ft

a manufacturer ships its product in boxes with edges of 4 inches. if 12 boxes are put in a carton and completely fill the carton, what is the volume of the carton?

hugo and ava each built a rectangular prism that has a length of 5 units, a width of 2 units, and a height of 4 units. hugo used cubes that are 1 cm on each side. ava used cubes that are 1 in. on each side. what is the volume of each prism?

Question

use the unit given. find the volume.
1.
each cube = 1 cu cm
volume = 105 cu cm
2.
8 in.
2 in.
3 in.
each cube = 1 cu in.
volume = __ cu __
3.
7 ft
4 ft
2 ft
each cube = 1 cu ft
volume = __ cu __
4.
5 cm
5 cm
5 cm
each cube = 1 cu cm
volume = __ cu __
5. compare the volumes. write <, >, or =
5 ft
3 ft
4 ft
each cube = 1 cu ft
__ cu ft __ __ cu ft
6 ft
5 ft
2 ft
each cube = 1 cu ft
6. a manufacturer ships its product in boxes with edges of 4 inches. if 12 boxes are put in a carton and completely fill the carton, what is the volume of the carton?
7. hugo and ava each built a rectangular prism that has a length of 5 units, a width of 2 units, and a height of 4 units. hugo used cubes that are 1 cm on each side. ava used cubes that are 1 in. on each side. what is the volume of each prism?

Accepted Answer

### Problem 2:
# Explanation:
## Step1: Identify the formula for the volume of a rectangular prism.
The volume $ V $ of a rectangular prism is given by $ V = l \times w \times h $, where $ l $ is the length, $ w $ is the width, and $ h $ is the height.
## Step2: Substitute the given values into the formula.
Here, $ l = 8 $ in, $ w = 2 $ in, and $ h = 3 $ in. So, $ V = 8 \times 2 \times 3 $.
## Step3: Calculate the product.
First, multiply $ 8 \times 2 = 16 $. Then, multiply $ 16 \times 3 = 48 $.
# Answer:
$ 48 $ cu in

### Problem 3:
# Explanation:
## Step1: Recall the volume formula for a rectangular prism.
The formula is $ V = l \times w \times h $, with $ l $ as length, $ w $ as width, and $ h $ as height.
## Step2: Plug in the values.
Given $ l = 7 $ ft, $ w = 4 $ ft, and $ h = 2 $ ft. So, $ V = 7 \times 4 \times 2 $.
## Step3: Compute the result.
First, $ 7 \times 4 = 28 $. Then, $ 28 \times 2 = 56 $.
# Answer:
$ 56 $ cu ft

### Problem 4:
# Explanation:
## Step1: Use the volume formula for a cube (a special case of a rectangular prism where $ l = w = h $).
The volume $ V $ of a cube is $ V = s \times s \times s $ (or $ V = s^3 $), where $ s $ is the length of a side.
## Step2: Substitute the side length.
Here, $ s = 5 $ cm. So, $ V = 5 \times 5 \times 5 $.
## Step3: Calculate the volume.
$ 5 \times 5 = 25 $, and $ 25 \times 5 = 125 $.
# Answer:
$ 125 $ cu cm

### Problem 5:
# Explanation:
## Step1: Calculate the volume of the first prism.
For the first rectangular prism, $ l = 5 $ ft, $ w = 3 $ ft, $ h = 4 $ ft. Using $ V = l \times w \times h $, we get $ V = 5 \times 3 \times 4 $.
## Step2: Compute the volume of the first prism.
$ 5 \times 3 = 15 $, and $ 15 \times 4 = 60 $ cu ft.
## Step3: Calculate the volume of the second prism.
For the second rectangular prism, $ l = 6 $ ft, $ w = 5 $ ft, $ h = 2 $ ft. Using $ V = l \times w \times h $, we get $ V = 6 \times 5 \times 2 $.
## Step4: Compute the volume of the second prism.
$ 6 \times 5 = 30 $, and $ 30 \times 2 = 60 $ cu ft.
## Step5: Compare the two volumes.
Since both volumes are $ 60 $ cu ft, they are equal.
# Answer:
$ 60 $ cu ft $ = $ $ 60 $ cu ft

### Problem 6:
# Explanation:
## Step1: Find the volume of one box (a cube).
The volume of a cube with edge length $ s = 4 $ inches is $ V_{\text{box}} = s \times s \times s = 4 \times 4 \times 4 $.
## Step2: Calculate the volume of one box.
$ 4 \times 4 = 16 $, and $ 16 \times 4 = 64 $ cubic inches per box.
## Step3: Find the volume of the carton (which holds 12 boxes).
Multiply the volume of one box by the number of boxes: $ V_{\text{carton}} = 64 \times 12 $.
## Step4: Compute the total volume.
$ 64 \times 12 = 768 $ cubic inches.
# Answer:
$ 768 $ cubic inches

### Problem 7:
# Explanation:
## Step1: Use the volume formula for a rectangular prism for each prism.
The volume $ V = l \times w \times h $, where $ l = 5 $ units, $ w = 2 $ units, $ h = 4 $ units.
## Step2: Calculate the volume (same for both, as the formula depends on dimensions, not the cube size for the prism's volume).
$ V = 5 \times 2 \times 4 $.
## Step3: Compute the volume.
$ 5 \times 2 = 10 $, and $ 10 \times 4 = 40 $. So, the volume of Hugo's prism (in cubic centimeters) is $ 40 $ cu cm, and Ava's prism (in cubic inches) is $ 40 $ cu in.
# Answer:
Hugo's prism: $ 40 $ cu cm; Ava's prism: $ 40 $ cu in

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QUESTION IMAGE

Question

Explanation:

Problem 2:

Step1: Identify the formula for the volume of a rectangular prism.

Step2: Substitute the given values into the formula.

Step3: Calculate the product.

Step1: Recall the volume formula for a rectangular prism.

Step2: Plug in the values.

Step3: Compute the result.

Step1: Use the volume formula for a cube (a special case of a rectangular prism where \( l = w = h \)).

Step2: Substitute the side length.

Step3: Calculate the volume.

Answer:

Problem 3: