calculus word problem

[dear2009]

Hey everybody,


Suppose a right circular cylinder’s radius is increasing at the rate of 4m/sec while its height is decreasing at the rate of 5m/sec. How fast is the cylinder’s volume changing when its radius is 20m and its height is 40m? (answers given are approximate, in units of cubic meters per second)


V = 10 m^3 / sec
diameter = height
1/3 (3.14)(r^2)(height) = 1/3 (3.14)(r^3)
V = 1/3(3.14)(h^3)

10 = dr/dt = 1/3(3.14) (3h^2)(dh/dt)
10 = 1/3(3/14)(dh/dt)
(1/2h^2)(20/3.14) = dh/dt

200 = 1/3(3.14)(h^3)
h^3 = 3 /200(3.14)

I dont know how to do the rest of this part so I was hoping for some help. Thanks in advance

 

[Deleted member 4993]

Hey everybody,


Suppose a right circular cylinder’s radius is increasing at the rate of 4m/sec while its height is decreasing at the rate of 5m/sec. How fast is the cylinder’s volume changing when its radius is 20m and its height is 40m? (answers given are approximate, in units of cubic meters per second)


V = 10 m^3 / sec
diameter = height
1/3 (3.14)(r^2)(height) = 1/3 (3.14)(r^3)
V = 1/3(3.14)(h^3)

10 = dr/dt = 1/3(3.14) (3h^2)(dh/dt)
10 = 1/3(3/14)(dh/dt)
(1/2h^2)(20/3.14) = dh/dt

200 = 1/3(3.14)(h^3)
h^3 = 3 /200(3.14)

I dont know how to do the rest of this part so I was hoping for some help. Thanks in advance

V = ? * r[sup:3uiuyb5q]2[/sup:3uiuyb5q] * h

dV/dt = ? * [2*r * h * (dr/dt) + r[sup:3uiuyb5q]2[/sup:3uiuyb5q] * (dh/dt)]

Now continue....

 

[dear2009]

Dear Subhotosh Khan,


Thanks for the reply, my TA used this equation but got weird results (they were completely way off the 5 given answers)

Can you please show me the next step of plugging in, I tried but to no success

 

[Deleted member 4993]

Hey everybody,


Suppose a right circular cylinder’s radius is increasing at the rate of 4m/sec while its height is decreasing at the rate of 5m/sec. How fast is the cylinder’s volume changing when its radius is 20m and its height is 40m? (answers given are approximate, in units of cubic meters per second)


V = 10 m^3 / sec
diameter = height
1/3 (3.14)(r^2)(height) = 1/3 (3.14)(r^3)
V = 1/3(3.14)(h^3)

10 = dr/dt = 1/3(3.14) (3h^2)(dh/dt)
10 = 1/3(3/14)(dh/dt)
(1/2h^2)(20/3.14) = dh/dt

200 = 1/3(3.14)(h^3)
h^3 = 3 /200(3.14)

I dont know how to do the rest of this part so I was hoping for some help. Thanks in advance

V = ? * r[sup:32uw6724]2[/sup:32uw6724] * h

dV/dt = ? * [2*r * h * (dr/dt) + r[sup:32uw6724]2[/sup:32uw6724] * (dh/dt)]

Now continue....

dV/dt = ? * [2*r * h * (dr/dt) + r[sup:32uw6724]2[/sup:32uw6724] * (dh/dt)]

= ? * [2*20 * 40 * (4) + 20[sup:32uw6724]2[/sup:32uw6724] * (-5)] = ? * 11 * 400 m/sec