Which volume amount matches each scenario?(3 points)

Question

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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?

Answer 1

To calculate the volume of each rectangular prism scenario, we can use the formula for the volume of a rectangular prism, which is:

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

or

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

Now, let's compute the volumes for each of the scenarios:

1. Large gift box (base area 15 sq ft, height 5 ft): \[ \text{Volume} = \text{Base Area} \times \text{Height} = 15 \text{ ft}^2 \times 5 \text{ ft} = 75 \text{ ft}^3 \]

2. Scuba diving lagoon (length 50 ft, width 20 ft, depth 25 ft): \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Depth} = 50 \text{ ft} \times 20 \text{ ft} \times 25 \text{ ft} = 25000 \text{ ft}^3 \]

3. Rectangular prism (length 7 ft, width 9 ft, height 12 ft): \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} = 7 \text{ ft} \times 9 \text{ ft} \times 12 \text{ ft} = 756 \text{ ft}^3 \]

Here are the corresponding volume amounts for each scenario:

1. Large gift box: 75 ft³
2. Scuba diving lagoon: 25000 ft³
3. Rectangular prism: 756 ft³