# The rate at which a spherical pill(table) dissolves in the body after being consumed is described by the rate of change of its volume with time dv/dt. given that the rate of change of volume is directly proportional to its surface area, compute the time in which 80% of a pill of size 4cm would dissolve, given that it dissolve completely in 2hrs.

1
by btudu5117

2015-09-20T02:52:18+05:30

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V = 4π R³ / 3  of a spherical pill
dV/ dt = 4 π R²  = surface area of sphere
let Z be a constant of proportionality.

Given  the size = diameter at t = 0 is,  4 cm.  So radius = 2 cm.
Volume  at t = 0, is  V₀ = 4 π (2)³ / 3 =  32π/3  cm³
Rate of change of Volume = d V / dt  = - Z * 4π R²  = - Z * S

Time to dissolve 80% of the pill = 0.83 * 60 = 49.8 minutes.

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