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Difficulty: HardRectangular Volume and Container Capacity

An engineering unit is excavating a rectangular trench that is 1212 yards long, 66 yards wide, and 99 feet deep. The excavated dirt will be removed using dump trucks. If each dump truck has a rectangular bed that measures 1212 feet long, 66 feet wide, and 33 feet deep, what is the total number of truckloads required to remove all the dirt from the trench?

  1. A
    81
  2. B
    9
  3. 27Answer
  4. D
    243

Answer

27
To find the number of truckloads, the total volume of the trench must be divided by the volume of one truck, ensuring all measurements use the same unit. Converting all dimensions to yards, the truck volume is 4×2×1=84 \times 2 \times 1 = 8 cubic yards, and the trench volume is 12×6×3=21612 \times 6 \times 3 = 216 cubic yards. Dividing 216216 by 88 yields exactly 2727 truckloads.

Step-by-Step Solution

1
Convert the dimensions of the dump truck bed from feet to yards.
Length = 44 yards, Width = 22 yards, Depth = 11 yard.
Standardizing all measurements to a single unit (yards) is necessary before volumes can be accurately compared.
2
Calculate the volume capacity of a single dump truck in cubic yards.
4×2×1=84 \times 2 \times 1 = 8 cubic yards.
Finding the volume of the rectangular bed determines exactly how much dirt one truck can haul per trip.
3
Convert the depth of the trench from feet to yards.
99 feet ÷3=3\div 3 = 3 yards.
The length and width are given in yards, so the depth must also be in yards to calculate the correct total volume.
4
Calculate the total volume of the rectangular trench in cubic yards.
12×6×3=21612 \times 6 \times 3 = 216 cubic yards.
Multiplying length by width by depth gives the total amount of dirt that needs to be removed.
5
Determine the total number of truckloads required.
216÷8=27216 \div 8 = 27 truckloads.
Dividing the total trench volume by the capacity of a single truck yields the required number of trips.

Key Concept

Calculating and comparing volumes of rectangular prisms while performing correct unit conversions between standard linear measurements.
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Topics

Rectangular Volume and Container Capacity

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