Question

Antarctica, almost completely covered in ice, has an area

of5,500,000 mi2 with an average height of 7500 ft.
Withoutthe ice, the height would only be 1500ft. Estimate the mass
of thisice. The Density of ice is 0.917 g/cm3.

Answer 1

Answer: The mass of ice is
`2.39* 10^(22)g`

Step-by-step explanation:

We are given:

Area of Antarctica =
`5,500,000mi^2=5,500,000* 2.59* 10^(10)=142.45* 10^(15)cm^2` (Conversion factor:
`1mi^2=2.59* 10^(10)cm^2` )

Height of Antarctica with ice = 7500 ft.

Height of Antarctica without ice = 1500 ft.

Height of ice = 7500 - 1500 = 6000 ft =
`182.88* 10^3cm` (Conversion factor: 1 ft = 30.48 cm)

To calculate mass of ice, we use the equation:

`\text{Density of a substance}=\frac{\text{Mass of a substance}}{\text{Volume of a substance}}`

We are given:

Density of ice =
`0.917g/cm^3`

Volume of ice = Area × Height of ice =
`142.45* 10^(15)cm^2* 182.88* 10^3cm=26051.26* 10^(18)cm^3`

Putting values in above equation, we get:

`0.917g/cm^3=\frac{\text{Mass of ice}}{26051.26* 10^(18)cm^3}\\\\\text{Mass of ice}=(0.917g/cm^3* 26051.26* 10^(18)cm^3=2.39* 10^(22)g`

Hence, the mass of ice is
`2.39* 10^(22)g`