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A spherical balloon is inflated so that its volume is increasing at the rate of 2.5 ft3/min. How rapidly is the diameter of the balloon increasing when the diameter is 1.3 feet?

Respuesta :

Answer:

.1177 ft/min

Step-by-step explanation:

Sphere volume = 4/3 pi r^3

dv/dr = 4/3 pi * 3 r ^2    = 4 pi r^2

dv/dr  * dr/dt =          dv/dt =  4 pi r^2  dr/dt

                                  2.5   = 4 pi (1.3)^2 dr/dt

                                 dr/dt = .1177  ft/min

 

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