Question

1. 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 40.0 feet wide by 80.0 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 has a volume of 600 cm³. 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?
(1 in = 2.54 cm) ________ dump-truck loads

2. What will be the cost of gasoline for a 1320-mile trip from Wytheville to Orlando in a car that gets 28.0 miles per gallon, if the average price of gas is $3.25 per gallon? $________

3. The density of silver is 10.5 g/cm³. Express this density in pounds per cubic inch. ft³ (1 in = 2.54 cm) (2.20 lb = 1 kg) ___lb/in³

Answer 1

1. Total Volume of dirt removed = l*b*h = 40*80*7.5 = 24000 cubic foot (1 foot = 30.48cm so 1 cubic foot = 28316.8 cubic cm)

   = 24000* 28316.8 = 67,96,03,200 cm³

Now 600cm³ of dirt weights 1kg so 67,96,03,200 cm³ will weight 67,96,03,200 cm³/ 600cm³ = 1132672 kg

1 truck can carry 8000kg of dirt

Total number of trucks required for 1132672kg = 1132672/8000 = 141.5 = 142 trucks.

2. With 1 gallon of gas car can move 28 miles so for 1320 mile trip gas required is 1320/28 gallons = 47.142gallon

Cost of 1 gallon = $3.25

Total cost for the trip = 47.142*3.25 = $153.21

3. 1000g = 2.2lb => 1g = 0.0022lb

1 inch = 2.54cm => 1 cm = 0.397 inch => 1cubic cm = 0.062 cubic inch

Density = 10.5*0.0022/ 0.062 = 0.37 lb/ cubic inch