To find the volume of the lagoon, we need to calculate the volume of the rectangular top and subtract the volume of the pyramid.
The volume of a rectangular prism is found by multiplying the length, width, and height. The top of the lagoon has dimensions of 50 ft by 20 ft, and the height of the prism is 25 ft.
Volume of rectangular prism = length * width * height
Volume of rectangular prism = 50 ft * 20 ft * 25 ft
Volume of rectangular prism = 50 * 20 * 25 = 25,000 ft^3
The volume of a pyramid is found by dividing the volume of the rectangular prism by 3.
Volume of pyramid = volume of rectangular prism / 3
Volume of pyramid = 25,000 ft^3 / 3 = 8,333.33 ft^3
To find the total volume of the lagoon, we subtract the volume of the pyramid from the volume of the rectangular prism.
Total volume = volume of rectangular prism - volume of pyramid
Total volume = 25,000 ft^3 - 8,333.33 ft^3
Total volume = 16,666.67 ft^3
So, the lagoon holds 16,666.67 ft^3 of water. Round to the nearest cubic foot, the answer is 16,667 ft^3.
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 75,000 ft.3 75,000 feet cubed 25,000 ft.3 25,000 feet cubed 95 ft.3 95 feet cubed 8,333.33 ft.3
5 answers
WRONG
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To find the volume of the lagoon, we can break it down into two sections: the rectangular top and the pyramidal bottom.
The volume of the rectangular section is calculated by multiplying the length, width, and height. In this case, the length is 50 feet, the width is 20 feet, and the height is 25 feet.
Volume of rectangular section = length * width * height
Volume of rectangular section = 50 ft * 20 ft * 25 ft
Volume of rectangular section = 25,000 ft^3
The volume of the pyramidal section can be calculated using the formula: (1/3) * base area * height. The base area of the pyramid is the same as the rectangular section, 50 ft by 20 ft, and the height is 25 ft.
Volume of pyramidal section = (1/3) * 50 ft * 20 ft * 25 ft
Volume of pyramidal section = 8,333.33 ft^3
To find the total volume of the lagoon, we add the volume of the rectangular section and the volume of the pyramidal section.
Total volume = volume of rectangular section + volume of pyramidal section
Total volume = 25,000 ft^3 + 8,333.33 ft^3
Total volume = 33,333.33 ft^3
So, the lagoon holds approximately 33,333.33 ft^3 of water.
To find the volume of the lagoon, we can break it down into two sections: the rectangular top and the pyramidal bottom.
The volume of the rectangular section is calculated by multiplying the length, width, and height. In this case, the length is 50 feet, the width is 20 feet, and the height is 25 feet.
Volume of rectangular section = length * width * height
Volume of rectangular section = 50 ft * 20 ft * 25 ft
Volume of rectangular section = 25,000 ft^3
The volume of the pyramidal section can be calculated using the formula: (1/3) * base area * height. The base area of the pyramid is the same as the rectangular section, 50 ft by 20 ft, and the height is 25 ft.
Volume of pyramidal section = (1/3) * 50 ft * 20 ft * 25 ft
Volume of pyramidal section = 8,333.33 ft^3
To find the total volume of the lagoon, we add the volume of the rectangular section and the volume of the pyramidal section.
Total volume = volume of rectangular section + volume of pyramidal section
Total volume = 25,000 ft^3 + 8,333.33 ft^3
Total volume = 33,333.33 ft^3
So, the lagoon holds approximately 33,333.33 ft^3 of water.
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 finding the volume of a pyramid is given by:
Volume = (1/3) * base area * height
We are given:
Length of the rectangular pyramid (l) = 7 cm
Width of the rectangular pyramid (w) = 9 cm
Volume (V) = 231 cubic centimeters
We can find the base area of the pyramid by multiplying the length and width:
Base area = l * w
Base area = 7 cm * 9 cm
Base area = 63 square centimeters
Now, we can rearrange the formula for the volume of a pyramid to solve for the height of the pyramid:
Volume = (1/3) * base area * height
Rearrange to solve for height:
Height = Volume / ((1/3) * base area)
Height = 231 cm^3 / ((1/3) * 63 cm^2)
Height = 231 cm^3 / (3/3 * 63 cm^2)
Height = 231 cm^3 / (63 cm^2)
Height = 3.6667 cm
Therefore, the height of the rectangular pyramid is approximately 3.67 cm.
Volume = (1/3) * base area * height
We are given:
Length of the rectangular pyramid (l) = 7 cm
Width of the rectangular pyramid (w) = 9 cm
Volume (V) = 231 cubic centimeters
We can find the base area of the pyramid by multiplying the length and width:
Base area = l * w
Base area = 7 cm * 9 cm
Base area = 63 square centimeters
Now, we can rearrange the formula for the volume of a pyramid to solve for the height of the pyramid:
Volume = (1/3) * base area * height
Rearrange to solve for height:
Height = Volume / ((1/3) * base area)
Height = 231 cm^3 / ((1/3) * 63 cm^2)
Height = 231 cm^3 / (3/3 * 63 cm^2)
Height = 231 cm^3 / (63 cm^2)
Height = 3.6667 cm
Therefore, the height of the rectangular pyramid is approximately 3.67 cm.