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;