Question
A spherical balloon is being inflated so that its volume is increasing
at a rate of 5 cubic feet /min.. At what rate is the diameter increasing
when the diameter is 12 feet?
at a rate of 5 cubic feet /min.. At what rate is the diameter increasing
when the diameter is 12 feet?
Answers
Anonymous
surface area of sphere = 4pi R^2, R = D/2 = 6
so
dV = 4 pi r^2 dr
dV/dt = 4pi r^2 dr/dt
5 ft^3/min = 4 pi (36) dr/dt
dr/dt = 5/ { 144 pi } = 0.011 ft/min
D = 2 r
so
d D/dt = 2 dR/dt
= 0.022 ft/min
so
dV = 4 pi r^2 dr
dV/dt = 4pi r^2 dr/dt
5 ft^3/min = 4 pi (36) dr/dt
dr/dt = 5/ { 144 pi } = 0.011 ft/min
D = 2 r
so
d D/dt = 2 dR/dt
= 0.022 ft/min