Plate tectonicsA simple model (see figure below) considers a continent as a block(density ≈2800kg/m3)floating in the mantle rock around it(density ≈3300kg/m3).Assuming the continent is 35 km thick (the average thickness of the Earth’s continental crust), estimate the height of the continent above the surrounding mantle rock.
Airy's Hypothesis was given by Sir George Biddell Airy, who was an English mathematician and astronomer. He assumed that the crustal density is uniform. Airy's Hypothesis explains that the Earth's crust floats over a substratum in a liquid state and has high density.
According to the question,
The density of the mantle $\left({\rho}_{m}\right)$ = 3300kg/cubic meters.
The density of the crust $\left({\rho}_{c}\right)$ =2800kg/cubic meters
The crustal thickness (t) = 35km or 35000 meters.
The relation gives the relation between the crustal root (r) and the height and thickness of the crust is given as, r=h+t
So, r=h+35000meters
From Airy's Hypothesis formula,
$r=\frac{h\times {\rho}_{c}}{{\rho}_{m}-{\rho}_{c}}\phantom{\rule{0ex}{0ex}}h+35000=\frac{h\times 2800}{3300-2800}\phantom{\rule{0ex}{0ex}}h+35000=\frac{h\times 2800}{500}\phantom{\rule{0ex}{0ex}}500h+17500000=2800h\phantom{\rule{0ex}{0ex}}\frac{17500000}{2300}=h\phantom{\rule{0ex}{0ex}}h=7608.696m\phantom{\rule{0ex}{0ex}}h=7.6km$
So, the height of the continent above the surrounding mantle rock is 7.6km