# Related rates of change.

• Jun 19th 2010, 02:31 AM
delicate_tears
Related 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 AM
sa-ri-ga-ma
What is the total surface area of the cylinder?

what is the volume of the cylinder?
• Jun 20th 2010, 01:17 PM
mfetch22
Quote:

Originally Posted by delicate_tears
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

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?