Answer:
m = 2.18x10¹⁵ tons of ice
Step-by-step explanation:
To solve this exercise, we need to work with the same units of conversion. In this case let's see the conversion of every unit here:
1 mi = 5280 ft
1 ton = 1000 kg
1 kg = 1000 g
1 mL = 1 cm³
1 mi = 1609.34 m or 160,934 cm
Now that we know the units, let's analyze the data.
The landscape has a 500,000 mi² of area, this is however without including the ice. The ice is apart, and has a 7520 ft of height. And if the landscape wouldn't have ice, then the height will be 1500 ft only.
With that data, we can know the actual height of the ice by a simple difference:
Hi = Hli - Hl
Where:
Hi: Height of ice
Hli: Height of ice + landscape
Hl: Height of landscape
Applying this expression, the height of ice is:
Hi = 7520 - 1500 = 6020 ft of ice
Now that we know the height of the ice, we can calculate the volume of whole landscape. But first, let's do the conversion of foot to mile:
Hi = 6020 ft * (1 mi/5280 ft) = 1.14 mi
And now, let's calculate the volume of the landscape in mile, and then, to centimeter:
V = 1.14 mi * 500,000 mi² = 570,000 mi³
To convert the cubic mile to cubic centimeter we just do the following:
V = 570,000 mi³ * (160934 cm / 1 mi)³ = 2.38x10²¹ cm³
Now, we can get the mass of the ice using the given density of ice (d = 0.917 g/cm³)
If d = m/V
then m = d * V
Replacing the data:
m = 0.917 g/cm³ * 2.38x10²¹ cm³
m = 2.18x10²¹ g
Finally, the tons of ice will be:
m = 2.18x10²¹ g * (1 kg / 1000 g) * (1 ton / 1000 kg)
m = 2.18x10¹⁵ tons of ice
Hope this helps