Each cubic centimeter of silver has a mass of 10.5 g.
(a) What is the mass of 62.9 cm3 of silver?
(b) When placed on a beam balance, the 62.9-cm3 piece of silver has a mass of only 612 g. What volume of the piece is hollow?
see post above
To find the mass of silver, you would multiply the volume of silver by its density. In this case, each cubic centimeter (cm3) of silver has a mass of 10.5 grams (g).
(a) To find the mass of 62.9 cm3 of silver, you would multiply the volume (62.9 cm3) by the density (10.5 g/cm3):
Mass = Volume x Density
Mass = 62.9 cm3 x 10.5 g/cm3
Mass = 659.45 grams
So, the mass of 62.9 cm3 of silver is 659.45 grams.
(b) To find the volume of the hollow part of the silver piece, you would subtract the mass of the hollow part from the total mass of the silver piece, and then divide by the density. The given total mass is 612 grams (g).
Let's denote the volume of the hollow part as Vh and the mass of the hollow part as Mh.
Mass of the silver piece - Mass of the hollow part = Mass of the solid part
Density x Volume of the solid part - Density x Volume of the hollow part = Mass of the solid part
Density x (Total Volume - Volume of the hollow part) - Density x Volume of the hollow part = Mass of the solid part
Density x Total Volume - Density x Volume of the hollow part - Density x Volume of the hollow part = Mass of the solid part
Density x Total Volume - 2 x Density x Volume of the hollow part = Mass of the solid part
Density x Total Volume = Mass of the solid part + 2 x Density x Volume of the hollow part
Volume of the hollow part = (Density x Total Volume - Mass of the solid part) / (2 x Density)
Plugging in the values:
Volume of the hollow part = (10.5 g/cm3 x 62.9 cm3 - 612 g) / (2 x 10.5 g/cm3)
Volume of the hollow part = (659.45 g - 612 g) / 21 g/cm3
Volume of the hollow part = 47.45 g / 21 g/cm3
Volume of the hollow part ≈ 2.26 cm3
So, the volume of the hollow part of the silver piece is approximately 2.26 cm3.