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?

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