How would you find the equation for the rate of change in volumes between two concentric spheres with progressing time given the radius as a function of time. I tried just subtracting the two volumes, but ofcourse thats wrong. In your answer please substitute the radius with r(t). Thanks.
2007-11-09 02:46:32 · 2 answers · asked by Ashton 2 in Science & Mathematics ➔ Mathematics
You want the rate of change of the difference of the two volumes. Let R = radius of larger sphere, and r = radius of the smaller sphere.
V= (4pi/3) [ R^2 -r^2 ]
dV/dt = (4pi/3) [ 2 R dR/dt - 2 r dr/dt]
to say anything further, you would need to be told something about the two radii R(t) and r(t) as functions of time.
2007-11-09 03:30:35 · answer #1 · answered by Michael M 7 · 0⤊ 0⤋
v = (4/3)pi r^3
Differentiate with respect to time t,
v' = 4pi r^2 r'
2007-11-09 02:54:29 · answer #2 · answered by sahsjing 7 · 0⤊ 0⤋