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What is the volume of a right rectangular prism with a length of 12, width of 5, and height of 10?(1 point)

___units cubed

2. What is the width of a rectangular prism with the volume of 100 units cubed, height of 10 units, and length of 5 units?(1 point)
___units

3. A rectangular prism has a base that is 15 units squared and a height of 5. What is its volume?(1 point)
___units cubed

4. A movie theater uses popcorn boxes in the shape of a right rectangular prism. Each box has a length of 9 inches, a width of 4 inches, and a height of 12 inches. What is the volume of popcorn the box can hold?(1 point)
___in.^3

5. A fish tank in the shape of a right rectangular prism has a volume of 1,920 cubic inches. What is the width of the tank if the height is 12 inches and the length is 20 inches?(1 point)
___in.

5 answers

  1. To find the volume of a right rectangular prism, you can use the formula:
    \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
    Given the dimensions,
    Length = 12, Width = 5, Height = 10:
    \[ \text{Volume} = 12 \times 5 \times 10 = 600 \text{ units cubed} \]
    Answer: 600 units cubed

  2. To find the width of a rectangular prism, you can rearrange the volume formula:
    \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
    Rearranging for Width:
    \[ \text{Width} = \frac{\text{Volume}}{\text{Length} \times \text{Height}} \]
    Given the volume of 100 cubic units, height of 10 units, length of 5 units:
    \[ \text{Width} = \frac{100}{5 \times 10} = \frac{100}{50} = 2 \text{ units} \]
    Answer: 2 units

  3. The volume of a rectangular prism can also be calculated using the formula:
    \[ \text{Volume} = \text{Base Area} \times \text{Height} \]
    Given the base area of 15 square units and height of 5:
    \[ \text{Volume} = 15 \times 5 = 75 \text{ units cubed} \]
    Answer: 75 units cubed

  4. To find the volume of the popcorn box, use the formula:
    \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
    Given the dimensions:
    Length = 9 inches, Width = 4 inches, Height = 12 inches:
    \[ \text{Volume} = 9 \times 4 \times 12 = 432 \text{ in.}^3 \]
    Answer: 432 in.^3

  5. To find the width of the fish tank, rearrange the volume formula:
    \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
    Rearranging for Width:
    \[ \text{Width} = \frac{\text{Volume}}{\text{Length} \times \text{Height}} \]
    Given the volume of 1,920 cubic inches, height of 12 inches, and length of 20 inches:
    \[ \text{Width} = \frac{1920}{20 \times 12} = \frac{1920}{240} = 8 \text{ in.} \]
    Answer: 8 in.

quick check:

1. Using the formula for the volume of a right rectangular prism, what is the area of the base when the volume is 50 cubic units and the height is 2?(1 point)
Responses

100 square units
100 square units

200 square units
200 square units

75 square units
75 square units

25 square units

2. The volume of a right rectangular prism is 1,000, the height is 10, and the length is 20. What is the width?(1 point)
Responses

50
50

15
15

200,000
200,000

5

3. Monica is constructing a box in the shape of a right rectangular prism to hold grain on her farm. Use the formula for the volume of a rectangular prism to find the area of the base when the volume is 50 cubic feet and the height is 4 feet.(1 point)
Responses

6.25 ft.2
6.25

ft.
2
6.25 feet squared

37.5 ft.2
37.5

ft.
2
37.5 feet squared

200 ft.2
200

ft
.
2
200 feet squared

12.5 ft.2
squared

4. Hakeem is building a box in the shape of a right rectangular prism to store his toys. It has a volume of 162,000 cubic centimeters. What is the width of the box if the height is 40 cm and the length is 90 cm?(1 point)
Responses

45 cm
45 cm

40 cm
40 cm

158,400 cm
158,400 cm

15 cm

5. Keysha needs to fill a container with cement. The container is in the shape of a right rectangular prism. The container has a length of 7.5 feet, a width of 5 feet, and a height of 3 feet. What is the volume of the container?(1 point)
Responses

1,125 ft.3
1
,
125

ft
.
3
1,125 feet cubed

15.5 ft.3
15.5

ft
.
3
15.5 feet cubed

112.5 ft.3
112.5

ft
.
3
112.5 feet cubed

37.5 ft.3
cubed

Let’s go through each question and find the correct answers step-by-step:

  1. Question: Using the formula for the volume of a right rectangular prism, what is the area of the base when the volume is 50 cubic units and the height is 2?
    Formula: Volume = Base Area × Height
    Rearranging for Base Area: Base Area = Volume / Height
    Calculation:
    \[ \text{Base Area} = \frac{50}{2} = 25 \text{ square units} \]
    Answer: 25 square units

  2. Question: The volume of a right rectangular prism is 1,000, the height is 10, and the length is 20. What is the width?
    Formula: Volume = Length × Width × Height
    Rearranging for Width: Width = Volume / (Length × Height)
    Calculation:
    \[ \text{Width} = \frac{1000}{20 \times 10} = \frac{1000}{200} = 5 \]
    Answer: 5

  3. Question: Monica is constructing a box in the shape of a right rectangular prism to hold grain on her farm. Use the formula for the volume of a rectangular prism to find the area of the base when the volume is 50 cubic feet and the height is 4 feet.
    Formula: Volume = Base Area × Height
    Calculation:
    \[ \text{Base Area} = \frac{50}{4} = 12.5 , \text{ft}^2 \]
    Answer: 12.5 ft.²

  4. Question: Hakeem is building a box in the shape of a right rectangular prism to store his toys. It has a volume of 162,000 cubic centimeters. What is the width of the box if the height is 40 cm and the length is 90 cm?
    Formula: Volume = Length × Width × Height
    Rearranging for Width: Width = Volume / (Length × Height)
    Calculation:
    \[ \text{Width} = \frac{162000}{90 \times 40} = \frac{162000}{3600} = 45 , \text{cm} \]
    Answer: 45 cm

  5. Question: Keysha needs to fill a container with cement. The container is in the shape of a right rectangular prism. The container has a length of 7.5 feet, a width of 5 feet, and a height of 3 feet. What is the volume of the container?
    Formula: Volume = Length × Width × Height
    Calculation:
    \[ \text{Volume} = 7.5 \times 5 \times 3 = 112.5 , \text{ft}^3 \]
    Answer: 112.5 ft.³

Feel free to ask if you need further clarification or assistance!

perfect ALL

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