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
problem 9: (7% of assignment value)
estimate the amount of water there could be in a global (planet - wide) region of subsurface permafrost on mar
surface of the planet. for these calculations, assume a permafrost thickness of 4.3 km and a concentration of ic

• part (a)

what is the surface area a of mars, in m², given that the planets radius r is 3395 km?
a = 1.44 * 10¹⁴
a = 1.440 × 10¹⁴ m² correct!

part (b)
what is the volume v of the permafrost zone, in m³?
v = m³

part (c)
if the ice is 10% by volume, what is the total mass m of ice in this layer, in kilograms? the density of water is 1

Explanation:

Step1: Convert thickness to meters

Given thickness \(h = 4.3\ km\). Since \(1\ km=1000\ m\), then \(h = 4.3\times10^{3}\ m\).

Step2: Use the formula for volume \(V = A\times h\)

We know from part (a) that \(A = 1.440\times 10^{14}\ m^{2}\).
Substitute \(A\) and \(h\) into the formula: \(V=(1.440\times 10^{14})\times(4.3\times 10^{3})\).
Using the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\) and \(a\times10^{m}\times b\times10^{n}=(a\times b)\times10^{m + n}\), we have \(V=(1.440\times4.3)\times10^{14 + 3}\).
\(1.440\times4.3 = 6.192\).

Answer:

\(6.192\times 10^{17}\ m^{3}\)