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A cube and a sphere of equal edge and ra...

A cube and a sphere of equal edge and radius, made of the same substance are allowed to cool under identical conditions. Determine which of the two will cool at a faster rate.

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The rate of cooling of a body is given by `(-dT)/(dt) = (Ae sigma)/( rho Vs) (T^(4) - T_(0)^(4))`
Since , substance is same for both bodies , so `(e)/(rho s)` = constant.
Further , they are allowed to cool under identical conditions , so `(T^(4) - T_(0)^(4)) ` = constant `therefore (-dT)/(dt) prop (A)/(V)`
Let the edge of the cube or radius of the sphere be a, then for the cube `A = 6a^(2)` and `V = a^(3) ` , so A/V = 6/a for the sphere , `A = 4pia^(2)` and `V = (4)/(3) pi a^(3)` , so A/V = 3/a.
Evidently , the ratio A/V is more for cube cools at a faster rate .
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