Question

Suppose a major impact blasted out rock from a 140-km-diameter crater that was, on average, 1 km deep. If all that material became dust that settled out evenly over the entire surface of the Earth, how thick a layer would it form?

The layer of dust would be about cm thick.

Answer 1

diameter of crater = 140 km

radius of crater (r)= 140/2 = 70 km = 7 x 10⁴ m

deepness of crater (d)= 1 km = 10³ m

now, volume of dust (V) = π r² d =π x (7 x 10⁴)² x 10³ = π x 49 x 10⁸ x 10³ =  π x 49 x 10¹¹ m³

now radius of earth (R) = 6,371 km = 6.371 x 10⁶ m

let the thickness of dust layer = t

now , 4 π R² t = V

or ,  4 x π x (6.371 x 10⁶ )² x t = π x 49 x 10¹¹

or, 4 x π x 39.9 x 10¹² x t = π x 49 x 10¹¹

or, t =  (49 x 10¹¹ ) / (4 x 39.9 x 10¹²) = 3.07 x 10^-2 m = 3.07 cm

hence, The layer of dust would be about 3.07 cm thick.