Implicit Differentiation of Cylinder NOT given radius?

[banfill_89]

Implicit Differentiation of Cylinder NOT given radius?

Homework Statement

Question: Digging in his backyard, Dennis accidentally breaks a pipe attached to his water sprinkling system. water bubbles up at a rate of 1 cm^3/s, forming a circular pond of depth 0.5cm in his yard. How quickly is the surface area of the pond covering his lawn?

Given: dV/dT= 1
depth= 0.5cm

RTF: dSA/Dt

Homework Equations

V= pi&r^2&h
SA= 2pi&r&h + 2pi&r^2

The Attempt at a Solution

i attempted a lot of things...i just always end up with the same problem: i don't know what r is or i can't find a way to relate r to anything.

 

[sutupidmath]

you don't actually need r at all.

$$V=Sh$$ this is the formula for calculating the volume of a cylindrical shape right? S- surface area, h- depth.
Use this info to find $$\frac{dS}{dt}$$ using the info you were given.

 

[tiny-tim]

Welcome to PF!

Homework Equations

V= pi&r^2&h
SA= 2pi&r&h + 2pi&r^2

Hi banfill_89! Welcome to PF!

First, you've missed out one relevant equation … what is V in terms of t?

And your SA equation is wrong … you're asked how fast the lawn is being covered. so you don't need the sides of the cylinder. And it's πr^2, not 2πr^2.

i attempted a lot of things...i just always end up with the same problem: i don't know what r is or i can't find a way to relate r to anything.

You have two equations for r … so you solve for r in the V equation (that is, you put "r =" on the left), and then you substitute that value of r into the SA equation.

You now have an SA equation with t but no r!

 

[banfill_89]

thanks

agh thanks a lot guys. i was heading in that direction too but my surface area equation was screwing me up. thanks for puttin me in the right direction