Question

an excavator is preparing to dig a basement for a new house. Part of his contract reads that he must dispose of all the dirt he removes while digging the basement in an EPA approved landfill. He will dig a hole that is 40 feet wide by 50 feet long and 7.5 feet deep. He first uses his shovel and scoops up 1.00 kg of dirt, and then determines that the dirt as a volume of 600 cm^3. The excavator knows that his dump truck can only carry 8,000 kg of dirt. How many dump-truck loads will it take to haul the dirt away?

Answer 1

Total Volume of dirt removed = l*b*h = 40×50×7.5 = 15000 cubic foot (1 foot = 30.48cm so 1 cubic foot = 28316.8 cubic cm)

   = 15000 × 28316.8 = 42,47,52,000 cm³

Now 600cm³ of dirt weights 1kg so 42,47,52,000 cm3 will weight= 424752000 cm³/ 600cm³ = 707920 kg

1 truck can carry 8000kg of dirt

Total number of trucks required for 707920kg = 707920/8000 = 88.5 = 89 trucks.

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