Answer:
d = 0.7857 feet
Explanation:
Volume = Length x Width x Depth
Volume = 10 feet x 8 feet x Depth
Volume = 80 Depth cubic feet
We don't know the volume of the bin, but we do know that it is completely filled. Therefore, we can assume that the volume of the bin is equal to its maximum capacity. In other words, the volume of the bin is the product of its length, width, and depth when it is filled to the top.
So, we can set the volume of the bin equal to its maximum capacity:
Volume = Length x Width x Depth
Volume = 10 feet x 8 feet x Depth
Volume = 80 Depth cubic feet = Maximum capacity
Let's assume the depth of the bin is d. Then we can write:
80d = Maximum capacity
We don't know the maximum capacity of the bin, but we know that it is completely filled. Therefore, the maximum capacity of the bin is equal to the actual volume of the material in the bin.
To find the depth, we need to know the material that is in the bin and its density. For example, we could assume that the bin is filled with water, which has a density of 62.4 pounds per cubic foot. If we convert the units, we get:
80d cubic feet x 62.4 pounds per cubic foot = Weight of water in the bin
Since the bin is completely filled, the weight of the water in the bin is equal to the weight of the bin itself. We don't know the weight of the bin, but we can assume that it is made of steel, which has a density of approximately 490 pounds per cubic foot. Therefore, we can write:
80d cubic feet x 62.4 pounds per cubic foot = Weight of bin
Weight of bin = Volume of bin x Density of steel
Weight of bin = (10 feet x 8 feet x d feet) x 490 pounds per cubic foot
Setting the two expressions for the weight of the bin equal to each other, we get:
80d x 62.4 = (10 x 8 x d) x 490
Simplifying this equation:
4992d = 3920d
d = 3920/4992
d = 0.7857 feet (approximately)