assume that all the energy (E) of the explosion is turned into kinetic

energy (KE) of the swept-up material.

mass M = (4/3) pi R^3 rho

avg velocity v = (R/t)

KE = (1/2) M * v^2 ~ R^3 rho (R^2 / t^2) ~ R^5 rho t^(-2)

So

E ~ R^5 rho t^(-2)

Re-arrange to solve for R

R ~ E^(1/5) rho^(-1/5) t^(2/5)

]]>Oops. Thank you. Now fixed.

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