## anonymous 5 years ago the radius of a copne is increasing at a rate of 3in/sec, and the height of the cone is 3 times the radius. Find the rate of change for the volume of that cone when the radius is 7 inches

1. nowhereman

So you know the volume of a cone is $$\frac{1}{3}πr^2h$$ so if as given $$h = 3r$$ you get $$V = πr^3$$. You also know that $$\dot{r} = 3in/s$$ and thus $$\dot{V} = 3πr^2\dot r$$ which for $$r = 7 in$$ gives you $$\dot V = 3^2\cdot 7^2πin^3/s$$.

2. anonymous

Some how I think that I am missing a step. [V=1\div3\times \Pi \times r^2\ times\h\] knowing that dr/dt = 3 in/sec h = 3r V =(3) * (1/3) * pi * r^2 * (dr/dt ) dv/dt =(3) * (1/3) * pi * r^2 * (3 )

3. anonymous