Calculate the mass in kilograms of gravel stored in a rectangular bin with the following dimensions:

- Length: 18.5 feet
- Width: 25.0 feet
- Depth: 15 feet

The density of the gravel is 97 pound-mass per cubic foot [lbm/ft^3]. Assume the gravel is flat on the top and neglect the space between the gravel pieces.

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.