The lagoon can be divided into three geometric shapes: two triangular prisms and one rectangular prism.
The volume of a rectangular prism is calculated by multiplying the length by the width by the height. In this case, the top of the lagoon is a rectangle that is 50 feet by 20 feet, so the area of the top surface is 50 x 20 = 1000 square feet. The height of the rectangular prism is 25 feet, so the volume is 1000 x 25 = 25,000 cubic feet.
The volume of a triangular prism is calculated by multiplying the area of the base by the height. In this case, the base of the triangular prism is a triangle with a base of 50 feet and a height of 25 feet (from the deepest point to the edge of the rectangle), so the area of the base is 0.5 x 50 x 25 = 625 square feet. The height of the triangular prism is 25 feet, so the volume is 625 x 25 = 15,625 cubic feet.
Since there are two triangular prisms, the total volume of the triangular prisms is 2 x 15,625 = 31,250 cubic feet.
Therefore, the total volume of the lagoon is 25,000 (rectangular prism) + 31,250 (triangular prisms) = 56,250 cubic feet.
So, the lagoon holds 56,250 cubic feet 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)
3 answers
incorrect do it again
I apologize for the mistake in my previous calculation. Let's try again:
The shape of the lagoon can be visualized as an upside-down pyramid, with the top being an area of 50 feet by 20 feet and the deepest point in the middle at 25 feet.
To find the volume of the lagoon, we first need to calculate the area of the top rectangle, which is 50 feet x 20 feet = 1000 square feet.
Since the lagoon is in the shape of an upside-down pyramid, the volume can be calculated using the formula for the volume of a pyramid: V = (1/3) x Area of base x Height.
The height of the pyramid-shaped lagoon is 25 feet.
Substitute the values into the formula:
V = (1/3) x 1000 square feet x 25 feet
V = (1/3) x 25,000 cubic feet
V = 8,333.33 cubic feet
Therefore, the lagoon holds approximately 8,333 cubic feet of water.
The shape of the lagoon can be visualized as an upside-down pyramid, with the top being an area of 50 feet by 20 feet and the deepest point in the middle at 25 feet.
To find the volume of the lagoon, we first need to calculate the area of the top rectangle, which is 50 feet x 20 feet = 1000 square feet.
Since the lagoon is in the shape of an upside-down pyramid, the volume can be calculated using the formula for the volume of a pyramid: V = (1/3) x Area of base x Height.
The height of the pyramid-shaped lagoon is 25 feet.
Substitute the values into the formula:
V = (1/3) x 1000 square feet x 25 feet
V = (1/3) x 25,000 cubic feet
V = 8,333.33 cubic feet
Therefore, the lagoon holds approximately 8,333 cubic feet of water.
2 answers