Question

A spherical balloon is inflated so that its radius (r) increases at a rate of 2/r cm/sec. How fast is the volume of the balloon increasing when the radius is 4 cm?

Answer 1

Answer:

Answer:

dv/dt

=32πcm3/s

 

dv/dt

=dv/dr*dr/dt

given:  

dr/dt

=2/r  cm/s

The volume of a sphere is:

v=4/3πr3cm3

dv/dr=4πr2  cm2

dv/dt=(4πr2  cm2)(2/r cm/s)

dv/dt=8πrcm3/s [1]

Evaluate equation [1] at  

r=4 cm

dv/dt

=32πcm3/s [2]

Step-by-step explanation: