Applications of antidifferentiation questions

[bloodninja21]

Hey guys, I'm halfway through practice questions, and I'm stuck:

~
Once the tanker is empty, the site foreman needs to assess the damage from the spill. First he puts down a layer of sawdust to absorb the petrol. Workers then use a series of vacuums to clean up the sawdust petrol mixture. One of the vacuums begins to malfunction, and the foreman examines the machine. On each of the vacuums there is a spherical balloon which helps control air flow. On the broken machine the balloon has sprung a leak. From an initial radius of 14cm, the radius is decreasing by a rate of 0.01cm per second.

A. Find an expression for the radius of the balloon (t) seconds after the leak began. Hence find an expression for the volume of the balloon (t) seconds after the leak began.

B. How many minutes does it take for the balloon to completely deflate

C. Find the rate at which the volume is decreasing 1 minute after the leak began. Round your answer to the nearest cm cubed

D. Show the rate of change of volume with respect to time is zero when the balloon is fully deflated.


Any help at all is greatly appreciated.

[tony3272]

A: r=14-0.01t

B: r=0, therefore 14-0.01t=0


C.    ,  ,

Using the Chain rule:



When t=60s, r= 14-0.01 x 60 =13.4cm





D. When t=1400s, r=0, when you sub in value of radius and time

[bloodninja21]

Thank you very much you're a lifesaver