A rectangular trench is to be dug which is to be 240 ft long, 90 ft wide and 9 ft deep. A large dump truck can carry 20 cubic yards in a load. How many truck loads will be required to remove the dirt from this trench?
To find the number of truck loads required to remove the dirt from the trench, we need to first calculate the volume of the trench and then divide that by the volume of each truck load.
Step 1: Calculate the volume of the trench.
Given:
Length of the trench = 240 ft
Width of the trench = 90 ft
Depth of the trench = 9 ft
Volume of the trench = Length × Width × Depth
Volume of the trench = 240 ft × 90 ft × 9 ft
Step 2: Convert the volume to cubic yards.
Since the truck load capacity is given in cubic yards, we need to convert the volume of the trench from cubic feet to cubic yards. There are 27 cubic feet in 1 cubic yard.
Volume of the trench (in cubic yards) = (240 ft × 90 ft × 9 ft) / (27 ft³/yard³)
Volume of the trench (in cubic yards) = 720 cubic yards
Step 3: Calculate the number of truck loads required.
Given:
Capacity of each truck load = 20 cubic yards
Number of truck loads = Volume of the trench / Capacity of each truck load
Number of truck loads = 720 cubic yards / 20 cubic yards
Number of truck loads = 36
Therefore, it will take 36 truck loads to remove the dirt from the trench.
To find the number of truck loads required to remove the dirt from the trench, we need to calculate the volume of the trench and then divide it by the capacity of the dump truck.
The volume of the rectangular trench can be calculated using the formula:
Volume = Length × Width × Depth
Given:
Length = 240 ft
Width = 90 ft
Depth = 9 ft
So, the volume of the trench is:
Volume = 240 ft × 90 ft × 9 ft
To convert the volume from cubic feet to cubic yards (which is the unit that the dump truck can carry), we need to divide the volume by 27 (since 3 feet = 1 yard and 3^3 = 27):
Volume in cubic yards = Volume in cubic feet / 27
Now, we can calculate how many truck loads will be required to remove the dirt by dividing the volume in cubic yards by the capacity of the dump truck (20 cubic yards/load):
Number of truck loads = Volume in cubic yards / Capacity of dump truck
Let's calculate the number of truck loads:
Volume = 240 ft × 90 ft × 9 ft = 194,400 cubic feet
Volume in cubic yards = 194,400 cubic feet / 27 = 7,200 cubic yards
Number of truck loads = 7,200 cubic yards / 20 cubic yards/load
Now, we can calculate the result:
Number of truck loads = 7,200 cubic yards / 20 cubic yards/load = 360 loads
Therefore, it would require 360 truck loads to remove the dirt from this trench.