A parabolic trough is 3 meters long, one foot across the top and one foot deep. Find the volume of water in the trough in liters if it is filled to a depth of 6inches.
To find the volume of water in the trough, we need to calculate the volume of a parabolic trough shape. The formula for the volume of a parabolic trough is given by:
V = (2/3) * length * (width^2) * depth
In this case, the length is 3 meters, which is equivalent to 3.28084 feet. The width is given as one foot, and the depth is given as 6 inches, which is equivalent to 0.5 feet.
First, we convert the length from meters to feet:
Length = 3 meters * 3.28084 feet/meter = 9.84252 feet
Now, we can calculate the volume of water in liters:
V = (2/3) * 9.84252 feet * (1 foot)^2 * 0.5 feet
V = (2/3) * 9.84252 * 1 * 0.5 cubic feet
Next, we need to convert the volume from cubic feet to liters.
1 cubic foot is equal to 28.3168466 liters, so:
V = (2/3) * 9.84252 * 1 * 0.5 * 28.3168466 liters
V ≈ 16.62320273 liters
Therefore, the volume of water in the trough, when filled to a depth of 6 inches, is approximately 16.62 liters.
To find the volume of water in the trough, we need to calculate the cross-sectional area of the trough and then multiply it by the length.
First, let's convert the given measurements into meters. Since 1 foot is approximately equal to 0.3048 meters, the dimensions of the trough are:
Length = 3 meters
Width (across the top) = 0.3048 meters
Depth = 0.3048 meters
To find the cross-sectional area of the trough, we'll use the formula for the area of a rectangle: Area = length × width.
Area = 3 meters × 0.3048 meters = 0.9144 square meters.
Now, let's convert the depth from inches to meters. Since 1 inch is equal to 0.0254 meters, the depth of 6 inches is:
Depth = 6 inches × 0.0254 meters/inch = 0.1524 meters.
The volume of water in the trough is given by the formula: Volume = Area × Depth.
Volume = 0.9144 square meters × 0.1524 meters = 0.13929104 cubic meters.
Finally, let's convert the volume from cubic meters to liters. Since 1 cubic meter is equal to 1000 liters, the volume in liters is:
Volume = 0.13929104 cubic meters × 1000 liters/cubic meter = 139.29104 liters (rounded to the nearest hundredth).
Therefore, the volume of water in the trough, when filled to a depth of 6 inches, is approximately 139.29 liters.