The base of a pyramid covers an area of 13.0 acres (1 acre = 43,560 ft2) and has a height of 481 ft. If the volume of a pyramid is given by the expression V = (1/3)bh, where b is the area of the base and h is the height, find the volume of this pyramid in cubic meters.

(1/3)(13ac*43560ft^2/ac)(480ft)(.3048m/ft)^3 = 2.5656*10^6 m^3

27700000

To find the volume of the pyramid in cubic meters, we need to convert the given area from acres to square meters.

Given:
Base area = 13.0 acres
1 acre = 43,560 ft^2
1 ft^2 = 0.09290304 m^2

To convert acres to square meters:
Area in square meters = (13.0 acres) * (43,560 ft^2/acre) * (0.09290304 m^2/ft^2)

Area in square meters = (13.0 * 43,560 * 0.09290304) m^2

Area in square meters = 53,713.59 m^2 (rounded to two decimal places)

Now, we can substitute the values into the volume formula to find the volume of the pyramid:

Volume = (1/3) * base area * height

Volume = (1/3) * 53,713.59 m^2 * 481 ft

Since we need the volume in cubic meters, we need to convert the height from feet to meters:

1 ft = 0.3048 m

Height = 481 ft * 0.3048 m/ft

Height = 146.5728 m

Now we can calculate the volume of the pyramid:

Volume = (1/3) * 53,713.59 m^2 * 146.5728 m

Volume = 3,927,287.802 cubic meters

Therefore, the volume of the pyramid is approximately 3,927,287.802 cubic meters.

To find the volume of the pyramid in cubic meters, we need to convert the given measurements to the appropriate units.

First, let's convert the area of the base from acres to square feet. We know that 1 acre is equal to 43,560 square feet, so the area of the base can be calculated by multiplying 13.0 acres by 43,560 square feet per acre:

Area of the base = 13.0 acres * 43,560 ft²/acre
= 566,280 ft²

Next, let's convert the height of the pyramid from feet to meters. We know that 1 meter is equal to 3.281 feet, so the height can be calculated by dividing 481 feet by 3.281 feet per meter:

Height of the pyramid = 481 ft / 3.281 ft/m
= 146.648 m

Now, we can calculate the volume of the pyramid using the formula V = (1/3)bh, where b is the area of the base and h is the height:

Volume of the pyramid = (1/3) * 566,280 ft² * 146.648 m
= 11021656.32 ft² * m

Finally, we need to convert the volume from cubic feet to cubic meters. We know that 1 cubic meter is equal to 35.3147 cubic feet, so we can calculate the volume in cubic meters by dividing the volume in cubic feet by 35.3147:

Volume of the pyramid in cubic meters = 11021656.32 ft² * m / 35.3147 ft³/m³
= 312254.9 m³

Therefore, the volume of the pyramid is approximately 312,254.9 cubic meters.