By any chance, has any0ne else worked this problem out and come with an answer of 8/405pi?
When I put the height as a function of the radius, I get h = 2/3r^2
so the volume = 2/9\pi h^3
when I differentiate both sides of the equation with respect to t, I get V\prime = 2/9\pi h^2 h\prime...
Since I am making the height as a function of the radius, I don't think I need to squlare the 1.5. Instead, if i just write [(2/3)πh^3]/3, or (2/9)πh^3, I can differentiate thar and hopefully I will get thte corect answer.
I have that. r Approximatelly equals 1.5h, however, I do not know how to find the rate of change for the radius with respect to time (dr/dt) in order to plug that into my equation and solve for the change in height with respect to time t (dh/dt). Since both radius and height change as the...
The problem states: sand falls onto a conical pile at a gravel yard at a rare of 10 cubic feet per minute. The base of the pile is approximately three times the altitude. How fast is the pile getting taller when the pile is 15 feet tall?Volume = πr² h/3
dV =...
I'm back and I've carefully checked to make sure I am reading it correctly.
First I set function in terms of y because of its rotation around the verticle axis, which gives me
y = sqrt(2x-2) Then I subtracted 3 because it revolves around x = 3. This is my radius, so I square it to get my...
Given this problem:
Find the volume and describe the shape of the object formed by the function f(x) = ½ x²+2 when the function is rotated around the x =3 axis and bounded by th region between the x = 0 and x = 4.
I am not sure if I am thihnking about this correctly. I know in order to...