The construction crew for a new store will dig a hole in the shape of a rectangular prism for the store's foundation. The hole will be
18yd
long,
15yd
wide, and
4yd
deep. To haul away all of the dirt from the hole, a dump truck will take trips to a nearby landfill. The crew knows the amount of dirt the truck can hold each trip in cubic feet.
(a) Find the volume of dirt that will be hauled away in cubic feet. Use the table of conversion facts, as needed.
ft3
(b) Each trip, the truck can haul away
295ft3
of dirt. To save gas, the crew wants to take as few trips as necessary to haul all of the dirt away. Since all of the dirt needs to be hauled away, the crew might have to take a partial load for one trip. How many trips are needed to haul away all of the dirt? Count each trip it makes the same, even if the truck isn't full.
trips
(c) If it costs
$1125
for each trip that the truck makes, how much will it cost to haul away all the dirt?
(a) To find the volume of dirt in cubic feet, we need to find the volume of the rectangular prism hole:
Volume = length x width x depth
Volume = 18 yd x 15 yd x 4 yd
Using the conversion 1 yard = 3 feet, we can convert to cubic feet:
Volume = (18 yd x 3 ft/yd) x (15 yd x 3 ft/yd) x (4 yd x 3 ft/yd)
Volume = 9720 ft^3
Therefore, the volume of dirt that needs to be hauled away is 9720 ft^3.
(b) Each trip can carry 295 ft^3 of dirt, so we can divide the total volume of dirt by the amount of dirt per trip to find the number of trips:
Number of trips = Volume of dirt / Amount of dirt per trip
Number of trips = 9720 ft^3 / 295 ft^3 per trip
Number of trips ≈ 32.94
Since we can't have a partial trip, we need to round up to 33 trips.
Therefore, it will take 33 trips to haul away all of the dirt.
(c) If it costs $1125 per trip, we can multiply the number of trips by the cost per trip to find the total cost:
Total cost = Number of trips x Cost per trip
Total cost = 33 trips x $1125 per trip
Total cost = $37,125
Therefore, it will cost $37,125 to haul away all of the dirt.
32.94 whole number
If we cannot have a partial trip, we need to round up to the nearest whole number, which is 33. Therefore, the crew needs to make 33 trips to haul away all of the dirt.
(a) To find the volume of dirt that will be hauled away in cubic feet, we first need to find the volume of the rectangular prism hole.
Volume of rectangular prism = length * width * height
Given:
Length = 18 yd
Width = 15 yd
Height = 4 yd
To convert the measurements to feet, multiply by the conversion factor: 1 yard = 3 feet
Length = 18 yd * 3 ft/yd = 54 ft
Width = 15 yd * 3 ft/yd = 45 ft
Height = 4 yd * 3 ft/yd = 12 ft
Volume = 54 ft * 45 ft * 12 ft
Calculating the volume:
Volume = 29160 ft^3
So, the volume of dirt that will be hauled away is 29160 ft^3.
(b) Each trip, the truck can haul away 295 ft^3 of dirt. To find the number of trips needed, we divide the total volume of dirt by the capacity of the truck.
Number of trips = Volume of dirt / Capacity of truck
Number of trips = 29160 ft^3 / 295 ft^3
Calculating the number of trips needed:
Number of trips ≈ 98.94915 trips (rounded up to the nearest whole number)
So, it will take approximately 99 trips to haul away all of the dirt.
(c) If each trip costs $1125, we can multiply the number of trips by the cost per trip to find the total cost.
Total cost = Number of trips * Cost per trip
Total cost = 99 trips * $1125
Calculating the total cost:
Total cost = $111,375
Therefore, it will cost $111,375 to haul away all of the dirt.