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We need to know about rate of change to solve the problem. The rate of change of volume of the sphere is 5026.55 sq/m.
Rate of change of a quantity is the rate at which it increases or decreases. It is given that the radius of the sphere increases at a rate of 1m/second. We need to find out the rate of change of volume of the sphere given the radius is 20m. We can calculate the rate of change of volume by calculating the derivative of volume with respect to time.
V=4/3[tex]\pi r^{3}[/tex]
dV/dt=4[tex]\pi r^{2}[/tex] dr/dt =4 x [tex]\pi[/tex]x20x20x1=5026.55 sq m/ second
Therefore the volume of the sphere increases at a rate of 5026.55 sq/m.
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