The volume of a cantaloupe is given by Upper V equals four thirds pi font size decreased by 5 r cubed . The radius is growing at the rate of 0.7 cm divided by week, at a time when the radius is 7.5 cm. How fast is the volume changing at that moment?

dV/dt = 494.8 cm^3 per week

the volume is changing at 494.8 cm^3 per week at that moment;

Completed question:

The volume of a cantaloupe is given by V = (4/3)πr^3 . The radius is growing at the rate of 0.7 cm/week, at a time when the radius is 7.5 cm. How fast is the volume changing at that moment?

Step-by-step explanation:

Given:

V = (4/3)πr^3

Radius r = 7.5 cm

dr/dt = 0.7cm/week

How fast is the volume changing at that moment;

dV/dt = d((4/3)πr^3)/dt

dV/dt = (4πr^2)dr/dt

Substituting the given values;

dV/dt = (4π×7.5^2)×0.7

dV/dt = 494.8 cm^3 per week

the volume is changing at 494.8 cm^3 per week at that moment;

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step-by-step explanation: