The density of silver is 1.050×104 kg/m3.
What is the mass of a rectangular ingot of silver with dimensions 1.00 cm × 4.00 cm × 0.780 dm?
How do I get started? I really do not understand.
Density is a measurement of mass per volume. In this example, density of silver is 1.050 x 10^4 kilogram per cubic meter (1 cubic meter silver would have 10500 kg mass).
You should solve for the volume of the ingot, then multiply by density to find mass.
ingot volume = 1.0 cm x 4.0 cm x 7.8 cm (1 dm = 10cm). = 54.6 cm^3. Since there are 1 million cm^3 in 1 m^3, 54.6 cm^3 multiplied by (1 m^3/1000000 cm^3) will give ingot volume in cubic meters, which is 5.46x10^-5 m^3 (0.0000546).
This volume x density looks like:
5.46x10^-5 m^3 x 1.050x10^4 kg/m^3 = 5.733x10^1 kg, which is also shown as 0.5733 kg.
Small correction...
For the final mass of silver, I intended to write 5.733x10^-1 kg, which is also shown as 0.5733 kg silver.
1.00 cm x 4.00 cm x 7.80 cm is not 54.7 cc is it? more like 31.2 cc.
Good catch DrBob. Fat fingers on calculator. Another reminder to check work.
To find the mass of the rectangular ingot of silver, we can use the formula:
mass = density * volume
To calculate the volume of the rectangular ingot, we multiply its length, width, and height:
volume = length * width * height
Now let's go step-by-step to solve this problem.
Step 1: Standardize the Units
First, we need to make sure that all the units are in the same system. In this case, we have centimeters (cm) and decimeters (dm). Since density is given in kg/m³, we need to convert the dimensions to meters (m).
1 cm = 0.01 m (since there are 100 centimeters in 1 meter)
1 dm = 0.1 m (since there are 10 decimeters in 1 meter)
So, the dimensions of the rectangular ingot in meters are:
length = 1.00 cm * 0.01 m/cm = 0.01 m
width = 4.00 cm * 0.01 m/cm = 0.04 m
height = 0.780 dm * 0.1 m/dm = 0.078 m
Step 2: Calculate the Volume
Now that we have all the dimensions in meters, we can calculate the volume:
volume = length * width * height = 0.01 m * 0.04 m * 0.078 m
Step 3: Calculate the Mass
Finally, we can calculate the mass using the given density:
mass = density * volume = 1.050 × 10^4 kg/m³ * (0.01 m * 0.04 m * 0.078 m)
Now, you can simply plug in the values and perform the calculations to find the mass of the rectangular ingot of silver.