Density is the amount of stuff inside a volume. In our case, our key equation looks like the following:
density = (mass\ of\ ice)/(volume\ of\ ice)
We are given the density as 0.617 g/cm^3. We want to find out the mass. To find the mass, we need to multiply our density by the total volume of ice.
Eq. 1. (density)*(volume\ of\ ice) = mass\ of\ ice
Thus, we need to follow the volume of ice and then convert everything into the proper units.
Let's find the volume of ice. We are told 82.4% of Finland is covered in ice. Thus, the actual area of Finland covered in ice is
82.4/100 * 2175000\ km^2 = 1792200\ km^2
Notice percentages have no units, so our answer of how much area is covered in ice remains in km^2.
Now that we have the area of ice covering Finland, we can find the volume. Because we are given the average depth of the ice sheet, we can assume the ice sheet looks roughly like a rectangular prism, or
The formula for find the volume of a rectangular prism is just area * height. We know the area, and we are given the height or depth as 7045m.
Volume\ of\ ice = 1792200\ km^2 * 7045m
Our units are no equivalent, so we'll need to convert meters into kilometers. There are 1000 meters in a kilometer
Volume\ of\ ice = 1792200\ km^2 * (7045m * (1km)/(1000m))
Volume\ of\ ice = 1792200\ km^2 * 7.045km
Volume\ of\ ice = 1792200\ km^2 * 7.045km
Volume\ of\ ice = 12626049\ km^3
Now that we have the volume of ice, we can get its mass using Eq. 1.
Eq. 1. (density) * (volume\ of\ ice) = mass\ of\ ice
Eq. 2. (0.617 g/(cm^3)) * (12626049\ km^3)
Our current units of cm^3 and km^3 cannot cancel out because they're not the same. We'll convert km^3 into cm^3. A single km is 1000m. 1m is in turn 100cm.
(cm)/(km) = (1km)/(1km) * (1000m)/(1km) * (100cm)/(1m)
There are 100000cm in 1km. To get how many cm^3 are in a single km^3, we just need to cube that number. So there are 1x10^15 cm^3 in 1km^3. Let's plug in this value to Eq. 2.
Eq. 3. (0.617 g/(cm^3)) * (12626049\ km^3) * 1x10^15 (cm^3)/(km^3)
By plugging in this value we cancel both km^3 and cm^3, which leaves us with just grams. However, we want the answer in kg. We know there are 1000g in 1kg, so let's also plug that into Eq. 3.
(0.617 g/(cm^3)) * (12626049\ km^3) * 1x10^15 (cm^3)/(km^3) * (1kg)/(1000g)
That allows us to cancel g and end up with kg, which concludes our dimension analysis.
Plugging these values into the calculator should give you the right answer! That's a ton of ice.
