A cylindrical container of fixed length 90 cm is being pressure tested, and the radious id increasing at a constant rate of .01 cm/min. WHen the redious is 25 cm, find the rate of the change of:

(a) the total surface area

(b) the Volume

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- Jun 19th 2010, 02:31 AMdelicate_tearsRelated rates of change.
A cylindrical container of fixed length 90 cm is being pressure tested, and the radious id increasing at a constant rate of .01 cm/min. WHen the redious is 25 cm, find the rate of the change of:

(a) the total surface area

(b) the Volume - Jun 19th 2010, 02:58 AMsa-ri-ga-ma
What is the total surface area of the cylinder?

what is the volume of the cylinder? - Jun 20th 2010, 01:17 PMmfetch22
So we have:

$\displaystyle V = (90)(\pi)(r^2)$

and

$\displaystyle SA = 2\pi r^2+2\pi r (90) $

For volume we have:

$\displaystyle \frac{dV}{dt} = (180)(\pi)(r)\frac{dr}{dt}$

At the values you gave we have:

$\displaystyle \frac{dV}{dt} = (180)(\pi)(25)(0.01)$

Thats the rate of change of the volume, can you figure it out the same way for surface area?