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.