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14 December, 20:23

A large sphere of material is placed in a dissolving liquid. (a) When the radius is 1 m, it is observed to be changing at 8 cm/hour. At that instant, what is the rate at which the sphere's volume is being dissolved with respect to time?

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  1. 14 December, 20:48
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    0.0804 m / h

    Explanation:

    r = 1 m, dr / dt = 8 cm/h = 0.08 m/h

    the volume of sphere is given by

    V = 4/3 x π x r^3

    Differentiate with respect to r.

    dV / dr = 4 / 3 x π x 3 r^2 x dr/dt

    dV/dt = 4 x π x r^2 x dr/dt

    dV/dt = 4 x 3.14 x 1 x 1 x 0.08

    dv/dt = 0.0804 m / h
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