When Rob was building his fish pond, he needed a truck to carry away the soil and rocks that he dug from the hole. The hole was 2.6 m by 1.9 m by 1.4 m. The weight of the soil and rocks averages 115 pounds per cubic foot.(Use 1 m = 3.3 ft)What will be the weight, in pounds, of the soil and rocks dug out for the fish pound?
Question
When Rob was building his fish pond, he needed a truck to carry away the soil and rocks that he dug from the hole. The hole was 2.6 m by 1.9 m by 1.4 m. The weight of the soil and rocks averages 115 pounds per cubic foot.(Use 1 m = 3.3 ft)What will be the weight, in pounds, of the soil and rocks dug out for the fish pound?
Solution
First, we need to convert the dimensions of the hole from meters to feet since the weight of the soil and rocks is given in pounds per cubic foot.
Given that 1 meter = 3.3 feet, we can convert as follows:
Length = 2.6 m * 3.3 ft/m = 8.58 ft Width = 1.9 m * 3.3 ft/m = 6.27 ft Height = 1.4 m * 3.3 ft/m = 4.62 ft
Next, we calculate the volume of the hole in cubic feet. The volume of a rectangular prism (which this hole is) is given by the formula length * width * height.
Volume = 8.58 ft * 6.27 ft * 4.62 ft = 197.67 cubic feet
Finally, we multiply the volume by the weight of the soil and rocks per cubic foot to find the total weight.
Weight = 197.67 cubic feet * 115 pounds/cubic foot = 22732.05 pounds
So, the weight of the soil and rocks dug out for the fish pond will be approximately 22732.05 pounds.
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