By immersing a crown in water its volume is 26inc^3=4.2x10^-4m^3. what would its weight be if it were pure gold?
What would its weight be if its volume were half gold and half lead?
To calculate the weight of the crown, we need to use the density of the material it is made of.
1. Weight of the crown if it were pure gold:
First, we need to find the volume of the crown in cubic meters (m³). The given volume is in cubic inches, so we need to convert it to cubic meters.
Given: Volume = 26 in³ = 4.2 x 10⁻⁴ m³
Now, the density of gold is approximately 19,300 kg/m³. We can multiply the volume of the crown by the density to find its mass.
Mass = Density x Volume
Mass = 19,300 kg/m³ x 4.2 x 10⁻⁴ m³
Therefore, the weight of the crown if it were made of pure gold can be calculated using the formula:
Weight = Mass x Acceleration due to gravity
2. Weight of the crown if its volume were half gold and half lead:
We need to consider the densities of both gold and lead to calculate the weight of the crown in this case.
The density of lead is around 11,340 kg/m³. Since the crown is half gold and half lead, we can find the volume of each material separately.
Volume of gold = (1/2) x Total Volume
Volume of lead = (1/2) x Total Volume
Now, we can find the masses of both gold and lead separately using their densities and volumes obtained above.
Mass of gold = Density of gold x Volume of gold
Mass of lead = Density of lead x Volume of lead
Finally, we can add the masses of gold and lead to find the total mass of the crown, and then calculate its weight using the formula mentioned earlier.
It is important to note that the acceleration due to gravity is approximately 9.8 m/s² for both calculations.