Answer:
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;
