Questions relating d/dt

[rafeeki92]

I have a thoughtful question...
The volume of a sphere is V = (4/3)pi(r^3), right?

So for a given dr/dx, where r = radius, Why is the rate of change of the volume of the sphere not constant even though dr/dt is constant?

 

[Deleted member 4993]

I have a thoughtful question...
The volume of a sphere is V = (4/3)pi(r^3), right?

So for a given dr/dx, where r = radius, Why is the rate of change of the volume of the sphere not constant even though dr/dt is constant?

Where is x coming from?

 

[rafeeki92]

oh so sorry, i meant dr/dt is constant

 

[rafeeki92]

i derived that

dV/dt = (4pi/3)(3r^2)(dr/dt)

not sure how to explain why dV/dt isn't constant

 

[BigGlenntheHeavy]

\(\displaystyle If \ the \ radius \ remains \ constant \ implies \ that \ there \ is \ no \ change \ in \ the \ radius \ in \ respect \ to\)

\(\displaystyle time, \ hence \ \frac{dr}{dt} \ = \ 0\)

\(\displaystyle V \ = \ \frac{4}{3}\pi r^{3}.\)

\(\displaystyle \frac{dV}{dt} \ = \ 4\pi r^{2}\frac{dr}{dt}, \ = \ 4\pi r^{2}(0) \ = \ 0, \ a \ constant.\)

 

[Deleted member 4993]

I have a thoughtful question...
The volume of a sphere is V = (4/3)pi(r^3), right?

So for a given dr/dt, where r = radius, Why is the rate of change of the volume of the sphere not constant even though dr/dt is constant?

Say

dr/dt = C[sub:2mbxoo4i]o[/sub:2mbxoo4i]

r = C[sub:2mbxoo4i]o[/sub:2mbxoo4i] * t + C[sub:2mbxoo4i]1[/sub:2mbxoo4i]

then

dV/dt = 4 * ? * r[sup:2mbxoo4i]2[/sup:2mbxoo4i] * (dr/dt) = 4 * ? * C[sub:2mbxoo4i]o[/sub:2mbxoo4i] * (C[sub:2mbxoo4i]o[/sub:2mbxoo4i] * t + C[sub:2mbxoo4i]1[/sub:2mbxoo4i])[sup:2mbxoo4i]2[/sup:2mbxoo4i] = f(t) ? 0

.