Question

problem set #7 begin date: 10/24/2025 12:01:00 am due date: 10/31/2025 11:59:00 pm end date: 11/2/2025 11:59:00 pm problem 9: (7% of assignment value) estimate the amount of water there could be in a global (planet - wide) region of subsurface permafrost on mars. that is, assume the permafrost is under the entire surface of the planet. for these calculations, assume a permafrost thickness of 4.3 km and a concentration of ice in the permafrost of 10% by volume. part (a) what is the surface area ( a ) of mars, in ( mathrm{m}^{2} ), given that the planets radius ( r ) is 3395 km? ( a=mathrm{m}^{2} ) part (b)

Explanation:

Step1: Recall the formula for the surface area of a sphere

The surface area formula for a sphere is \(A = 4\pi R^{2}\).

Step2: Convert the radius from kilometers to meters

Given \(R=3395\space km = 3395\times10^{3}\space m\).

Step3: Substitute the value of \(R\) into the formula

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Calculate \(3395^{2}=3395\times3395 = 11526025\).
Then \(A = 4\pi\times11526025\times10^{6}\).
Using \(\pi\approx3.14159\), we have \(A=4\times3.14159\times11526025\times 10^{6}\).

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\(12.56636\times11526025\approx1.44\times10^{8}\).
So \(A\approx1.44\times10^{14}\space m^{2}\).

Answer:

\(1.44\times 10^{14}\)