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Answer :
Final answer:
The mass of gravel in the rectangular bin with dimensions 18.5 feet by 25.0 feet and a depth of 15 feet, having a density of 97 lbm/ft³, is 305,025.92 kg when converted from pounds.
Explanation:
To calculate the mass of gravel stored in a bin, we need to follow these steps:
- Calculate the volume of the gravel bin.
- Convert the volume from cubic feet to cubic meters.
- Multiply the volume by the density to get the mass in pounds.
- Convert the mass from pounds to kilograms.
The volume V of the rectangular bin is found by multiplying its length l, width w, and depth d:
V = l × w × d
V = 18.5 ft × 25.0 ft × 15 ft
V = 6937.5 ft³
Convert this volume into cubic meters:
V = 6937.5 ft³ × 0.0283168 m³/ft³
V = 196.35 m³
The mass m in pounds is:
m = pV
m = 97 lbm/ft³ × 6937.5 ft³
m = 672534.25 lbm
Convert the mass to kilograms:
m = 672534.25 lbm × 0.453592 kg/lbm
m = 305,025.92 kg
The mass of gravel in the bin, in kilograms, is therefore 305,025.92 kg.
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