To find the volume of the lagoon, we need to calculate the volume of each section and then add them together.
First, let's calculate the volume of the rectangular top section. Since it is a rectangular prism, the volume is given by length × width × height. The height is 25 feet (the depth of the lagoon).
Volume of rectangle = 50 ft × 20 ft × 25 ft = 25,000 ft³
Next, let's calculate the volume of the bottom section. It is also a rectangular prism with the same length and width as the top, but half the height.
Volume of bottom section = 50 ft × 20 ft × 12.5 ft = 12,500 ft³
Finally, let's add the volumes of the top and bottom sections to find the total volume of the lagoon.
Total volume = Volume of rectangle + Volume of bottom section = 25,000 ft³ + 12,500 ft³ = 37,500 ft³
Therefore, the lagoon can hold 37,500 ft³ of water.
A resort is building a scuba diving lagoon in the shape of an upside down pyramid. The top of the lagoon is a rectangle that is 50 feet by 20 feet, and the deepest point of the lagoon is in the middle at 25 feet deep. How much water does the lagoon hold?(1 point)
Responses
8,333.33 ft.3
8,333.33 feet cubed
75,000 ft.3
75,000 feet cubed
95 ft.3
95 feet cubed
25,000 ft.3
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The answer you provided is: 25,000 ft³
A rectangular pyramid has a length of 7 cm and a width of 9 cm. Its volume is 231 cubic centimeters. Use the formula for the volume of a pyramid to calculate the height of this pyramid. Show all your work.(2 points)
The formula for the volume of a rectangular pyramid is given by V = (1/3) × base area × height.
Given:
Length (l) = 7 cm
Width (w) = 9 cm
Volume (V) = 231 cubic cm
We need to find the height (h).
First, let's calculate the base area. The formula for the area of a rectangle is given by A = length × width.
Base area = l × w = 7 cm × 9 cm = 63 square cm
Now, we can substitute the values into the volume formula and solve for the height:
V = (1/3) × base area × height
231 = (1/3) × 63 × h
To isolate h, divide both sides of the equation by (1/3) × 63:
231 ÷ ((1/3) × 63) = h
231 ÷ 21 = h
11 = h
Therefore, the height of the pyramid is 11 cm.
Given:
Length (l) = 7 cm
Width (w) = 9 cm
Volume (V) = 231 cubic cm
We need to find the height (h).
First, let's calculate the base area. The formula for the area of a rectangle is given by A = length × width.
Base area = l × w = 7 cm × 9 cm = 63 square cm
Now, we can substitute the values into the volume formula and solve for the height:
V = (1/3) × base area × height
231 = (1/3) × 63 × h
To isolate h, divide both sides of the equation by (1/3) × 63:
231 ÷ ((1/3) × 63) = h
231 ÷ 21 = h
11 = h
Therefore, the height of the pyramid is 11 cm.
1 answer