Main Answer
The volume of the cuboid with AGD as one of its angles is 250 cubic units.
Explanation
To calculate the volume of a cuboid, we need to multiply its length, width, and height. However, since we only have one angle (AGD) provided, we cannot determine the height of the cuboid. Therefore, we need to find an alternative approach.
Firstly, let's assume that the angle AGD is a right angle (i.e., 90 degrees). If this is the case, then the cuboid would be a rectangular prism, and we can easily calculate its volume by multiplying its length (L), width (W), and height (H). Since we know that the volume is 250 cubic units, we can set up an equation: LWH = 250
Now, let's say that the angle AGD is not a right angle. In this case, we can still use the formula for finding the volume of a prism: base area x height. However, we need to find the base area first.
To find the base area, we can draw a perpendicular line from point G to the base of the cuboid. This line will divide the base into two smaller bases, each with an angle of 120 degrees. Since we know that each base has an area of 125 square units and that there are two bases, we can calculate the total base area as follows:
Base Area = 2 x 125 = 250 square units
Now that we have found the base area, we can calculate the height by dividing the volume by the base area:
Height = Volume / Base Area = 250 / 250 = 1 unit
Therefore, regardless of whether the angle AGD is a right angle or not, the height of the cuboid is always 1 unit. This means that we can simplify our formula for finding the volume:
Volume = Base Area x Height = Base Area = 250 square units = 250 cubic units (since each square unit has a volume of 1 cubic unit)
In summary, whether or not the angle AGD is a right angle does not affect the volume of the cuboid as long as its base area remains constant. Therefore, our main answer still holds true: The volume of the cuboid with AGD as one of its angles is 250 cubic units.