Question

The radius of a spherical balloon is increasing at the rate of 0.4 cm divided by minute0.4 cm/minute. How fast is the volume changing when the radius is 7.47.4 ​cm?

Answer 1

dr/dt = 0.4
v = 4/3 pi r^3
dv/dr = 4 pi r^2
dv/dt = dv/dr * dr / dt = 4/0.4 pir^2 = 10 pi r^2
When radius is 7.4 volume is increasing by:-
dv/dt = 10pi7.4^2 = 1720.34 cm^3 / minute Answer