Related rates: volume of paint in right cylindrical can

[bobers]

The volume of paint in a right cylindrical can is given by V=4t^2-t where t is time in seconds and V is the volume in cm^3. How fast is the level rising when the height is 2cm? The can has a height of 4cm and a radius of 2cm.

I know that V=h(pi)r^2 for a cylinder
dv/dt=pi(2r(dr/dt)+r^2(dh/dt)
also dv/dt=8t-1
how do you find dr/dt and t

 

[wjm11]

Re: Related rates help

The volume of paint in a right cylindrical can is given by V=4t^2-t where t is time in seconds and V is the volume in cm^3. How fast is the level rising when the height is 2cm? The can has a height of 4cm and a radius of 2cm.

Some things to think about: this is a cylinder, not a cone; the radius is constant. Do not treat r as a variable.

For volume, plug in r = 2 and h = 2. Next, solve the quadratic for t.

Can you take it from there?