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A spherical balloon is being inflated so that its volume is increasing at the rate of 5 cubic meter per minute At what rate is the diameter increasing when the diameter is 12 meter?
Wiki User
∙ 15y ago
V = 4/3*pi*r^3dV/dt = 4/3*pi*3*r^2*dr/dt = 4*pi*r^2*dr/dt
Therefore dV/dt = 5 => 4*pi*r^2*dr/dt = 5
therefore dr/dt = 5/(4*pi*r^2)
Diameter = 12 metres => radius = 6 metres
So dr/dt = 5/(4*pi*36) = 0.01105 metres per minute.
diameter = 2*radius => rate of change of diameter = 0.2210 metres per minute.
Wiki User
∙ 9y ago
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