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Which volume amount matches each scenario?(3 points)

A large gift box is being constructed in the shape of a rectangular prism. The base area is 15 feet squared and the height is 5 feet. What will the volume of the gift box be?

A resort is building a scuba diving lagoon in the shape of a rectangular prism. The length is 50 feet, width 20 feet, and it is 25 feet deep. How much water does the lagoon hold?

A rectangular prism has a length of 7 ft, a width of 9 ft and a height of 12ft. What is the volume?

25,000ft3, 756ft3, 75ft3

1 answer

To find the volume of the rectangular prisms in each scenario, we can use the formula for the volume of a rectangular prism:

\[ \text{Volume} = \text{Base Area} \times \text{Height} \]

or

\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]

Now, let's calculate the volume for each scenario:

  1. Large gift box:

    • Base Area = 15 ft²
    • Height = 5 ft \[ \text{Volume} = 15 \text{ ft}^2 \times 5 \text{ ft} = 75 \text{ ft}^3 \]

  2. Scuba diving lagoon:

    • Length = 50 ft
    • Width = 20 ft
    • Depth (Height) = 25 ft \[ \text{Volume} = 50 \text{ ft} \times 20 \text{ ft} \times 25 \text{ ft} = 25,000 \text{ ft}^3 \]

  3. Rectangular prism:

    • Length = 7 ft
    • Width = 9 ft
    • Height = 12 ft \[ \text{Volume} = 7 \text{ ft} \times 9 \text{ ft} \times 12 \text{ ft} = 756 \text{ ft}^3 \]

Now that we have calculated the volumes:

  • The large gift box has a volume of 75 ft³.
  • The scuba diving lagoon holds 25,000 ft³ of water.
  • The other rectangular prism has a volume of 756 ft³.

So the volumes match as follows:

  • Large gift box: 75 ft³
  • Scuba diving lagoon: 25,000 ft³
  • Rectangular prism: 756 ft³