20. To find the weight of the remainder of the bar, we need to subtract the weight of the two cut pieces from the original weight of the bar:
Weight of the remainder = Original weight of the bar - (Weight of cut piece 1 + Weight of cut piece 2)
Weight of the remainder = 384/5 lbs - (13/8 lbs + 13/8 lbs)
Performing the calculations:
Weight of the remainder = 384/5 lbs - (13/8 lbs + 13/8 lbs)
Weight of the remainder = 384/5 lbs - 26/8 lbs
Weight of the remainder = 384/5 lbs - 13/4 lbs
Weight of the remainder = (384 * 4)/(5 * 4) lbs - 13/4 lbs
Weight of the remainder = 1536/20 lbs - 13/4 lbs
Weight of the remainder = 76.8 lbs - 3.25 lbs
Weight of the remainder = 73.55 lbs
Therefore, the weight of the remainder of the bar is approximately 73.55 lbs.
21. To find the length of the remaining piece of steel, we need to subtract the total length of the three pieces to be cut from the original length of the bar, accounting for the width of the cuts:
Remaining length = Original length - (Length of cut piece 1 + Length of cut piece 2 + Length of cut piece 3 - Total width of cuts)
Remaining length = 147/8 inches - (33/4 inches + 33/4 inches + 33/4 inches - 1/16 inches)
Performing the calculations:
Remaining length = 147/8 inches - (33/4 inches + 33/4 inches + 33/4 inches - 1/16 inches)
Remaining length = 147/8 inches - 99/16 inches + 1/16 inches
Remaining length = (147 * 2)/(8 * 2) inches - 99/16 inches + 1/16 inches
Remaining length = 294/16 inches - 99/16 inches + 1/16 inches
Remaining length = (294 - 99 + 1)/16 inches
Remaining length = 196/16 inches
Remaining length = 12.25 inches
Therefore, the remaining piece of steel is 12.25 inches long.
22. The wall thickness of the pipe can be calculated by subtracting the inside diameter from the outside diameter:
Wall thickness = Outside diameter - Inside diameter
Wall thickness = 4.375 inches - 3.875 inches
Performing the calculations:
Wall thickness = 4.375 inches - 3.875 inches
Wall thickness = 0.5 inches
Therefore, the wall thickness of the pipe is 0.5 inches.
23. The weight of the casting can be calculated by multiplying its volume by the weight per cubic inch of the material:
Weight of casting = Volume of casting * Weight per cubic inch
Weight of casting = 43.25 cubic inches * 0.26 lb/cubic inch
Performing the calculations:
Weight of casting = 43.25 cubic inches * 0.26 lb/cubic inch
Weight of casting = 11.245 lbs
Therefore, the weight of the casting is approximately 11.245 lbs.
24. To find the weight of 4.18 cubic feet of liquid, we need to multiply the volume by the weight per cubic foot:
Weight = Volume * Weight per cubic foot
Weight = 4.18 cubic feet * 62.5 lbs/cubic foot
Performing the calculations:
Weight = 4.18 cubic feet * 62.5