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?
(a) To find the mass of 62.9 cm³ of silver, we can use the given information that each cubic centimeter of silver has a mass of 10.5 g.
Mass = Volume × Mass per unit volume
Mass = 62.9 cm³ × 10.5 g/cm³
Mass = 659.45 g
Therefore, the mass of 62.9 cm³ of silver is 659.45 g.
(b) To find the volume of the hollow section, we need to compare the actual mass of the silver piece to the expected mass based on its volume.
Expected mass = Volume × Mass per unit volume
Expected mass = 62.9 cm³ × 10.5 g/cm³
Expected mass = 659.45 g
The actual mass of the silver piece is given as 612 g.
Let's assume the volume of the solid part of the silver piece is x cm³.
So, the volume of the hollow part of the silver piece would be (62.9 cm³ - x cm³).
Now, based on the mass, we can set up the equation:
Actual mass = Mass of the solid part + Mass of the hollow part
612 g = x cm³ × 10.5 g/cm³ + (62.9 cm³ - x cm³) × 0 g/cm³
612 g = 10.5x + 0
Simplifying the equation:
10.5x = 612
x = 612 / 10.5
x = 58.286 cm³
Therefore, the volume of the hollow section is approximately 58.286 cm³.
To get the answers to the questions, we need to use the given information that each cubic centimeter of silver has a mass of 10.5 g.
(a) To find the mass of 62.9 cm3 of silver:
We can multiply the volume of 62.9 cm3 by the mass per cubic centimeter.
Mass = Volume * Mass per cubic centimeter
Mass = 62.9 cm3 * 10.5 g/cm3
Mass = 659.85 g
Therefore, the mass of 62.9 cm3 of silver is 659.85 g.
(b) To determine the volume of the hollow part:
We are given that the entire piece of silver has a volume of 62.9 cm3 and a mass of 612 g.
Let's assume the volume of the hollow part is represented by V (in cm3).
The mass of the solid part can be calculated using the mass per cubic centimeter:
Mass of solid part = Volume of solid part * Mass per cubic centimeter
Mass of solid part = (62.9 cm3 - V) * 10.5 g/cm3
Now, we can set up an equation by adding the mass of the solid part and the mass of the hollow part, which is equal to the total mass given:
(62.9 cm3 - V) * 10.5 g/cm3 + V * 0 g/cm3 = 612 g
Simplifying the equation, we get:
657.45 g - 10.5V + 0V = 612 g
-10.5V = -45.45 g
V = -45.45 g / -10.5 g/cm3
V ≈ 4.33 cm3
Therefore, the volume of the hollow part in the 62.9 cm3 piece of silver is approximately 4.33 cm3.
mass=density*volume=10.5g/cc* 62.9cc
volumehollow=mass/density=1.7g/(10.5g/cc)