The volume of a sphere is expanding where r = 3t + 1. What is the rate of change volume with respect to time when t = 2? The volume of a sphere is V = (4π r^3)/3
-
V = (4*pi)/3)*(3t +1)^3
dV/dt = (4*pi/3)*[3(3t+1)^2]
dV/dt = (4*pi)*(3t +1)^2
= 4*pi(3t + 1)^2
When t = 2 dV/dt = 4*pi*49 = 196pi.
dV/dt = (4*pi/3)*[3(3t+1)^2]
dV/dt = (4*pi)*(3t +1)^2
= 4*pi(3t + 1)^2
When t = 2 dV/dt = 4*pi*49 = 196pi.