Cylinder derivative problem

[dear2009]

hello everyone,


Suppose a right circular cylinder’s radius is increasing at the rate of 10cm/sec while its height is decreasing at the rate of 19cm/sec. How fast is the cylinder’s volume changing when its radius and height are both 60cm? (approximately, in units of cubic centimeters per second).


This is how its to supposed to setup
r = 60
h = 60
dr/dt = + 10
dh/dt = -19

dV/dt = pi (d/dt) (r^2)(h) = pi (d/dt r^2)h + r^2 d/dt
this is how solved it, pi(60)(120)(10)(60)(19)

after this I didnt get the answer, so can I get some help on this problem

 

[wjm11]

Suppose a right circular cylinder’s radius is increasing at the rate of 10cm/sec while its height is decreasing at the rate of 19cm/sec. How fast is the cylinder’s volume changing when its radius and height are both 60cm? (approximately, in units of cubic centimeters per second).


This is how its to supposed to setup
r = 60
h = 60
dr/dt = + 10
dh/dt = -19

dV/dt = pi (d/dt) (r^2)(h) = pi (d/dt r^2)h + r^2 d/dt
this is how solved it, pi(60)(120)(10)(60)(19)

Focus on your last step. What happened to the + sign? What happened to r^2? What happened to the - sign?

You're almost there.

 

[dear2009]

Dear wjm11,



Thanks for the reply. So I do I just use the equation: dV/dt = pi (d/dt) (r^2)(h) = pi (d/dt r^2)h + r^2 d/dt

This is the correct equation right?

 

[wjm11]

dV/dt = pi (d/dt) (r^2)(h) = pi (d/dt r^2)h + r^2 d/dt

V = (pi)(r^2)(h)
dV/dt = (pi)[(r^2)(dh/dt) + h(2r)(dr/dt)]