Rates of Change involving Surface Area and Volume (1 Viewer)

[megan09]

hi, i'm having some trouble with a rates of change question that involves the rate of change of the surface area of a bubble and then having to calculate the rate of change of volume:

the surface area of a spherical bubble is increasing at a constant rate of 1.9 mm^2/s. find the rate of increase in its volume when its radius is 0.6 mm.

any help would be appreciated, thanks

 

[GUSSSSSSSSSSSSS]

well here u just use chain rule twice:

im guessing the bubble is spherical??

so the formulas:

V = (4/3).pi.r^3

and SA = 4.pi.r^2



hope that little bit helps...

 

[megan09]

hi thanks:

i first used:
da/dt = da/dr . dr/dt to get dr/dt = da/dt / da/dr

then subed this into :

dv/dt = dv/dr . dr/dt


and got the right answer! (o.57 mm^3 /s) thanks

 

[GUSSSSSSSSSSSSS]

yea perfect!!!!!!!!!