The volume of a cantaloupe is approximated by upper v equals four thirds pi font size decreased by 5 r cubedv= 4 3π r3. the radius is growing at the rate of 0.5 cm divided by week0.5 cm/week, at a time when the radius is 5.85.8 cm. how fast is the volume changing at that moment?

68.445 cm³/s

Explanation:

Given:

Volume, V =

radius = 5.85 cm

Growth rate of radius = 0.5 cm/week

now

differentiating the volume with respect to time 't', we get:

or

now, substituting the value of r (i.e at r = 5.85cm) in the above equation, we get:

or

hence, the rate of change of volume at r = 5.85cm is 68.445 cm³/s

0.19 m/s and 0.45 m/s