SOLUTION: The radius of a spherical balloon is increasing at a rate of 7 cm per second. Derive the composite function, V(t), for the volume of the balloon in terms of time t and use it to de

Algebra ->  Functions -> SOLUTION: The radius of a spherical balloon is increasing at a rate of 7 cm per second. Derive the composite function, V(t), for the volume of the balloon in terms of time t and use it to de      Log On


   

Question 764104: The radius of a spherical balloon is increasing at a rate of 7 cm per second. Derive the composite function, V(t), for the volume of the balloon in terms of time t and use it to determine the volume of the balloon after 8 seconds. Thanks for any help.
Answer by Alan3354(69443) About Me  (Show Source):
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The radius of a spherical balloon is increasing at a rate of 7 cm per second. Derive the composite function, V(t), for the volume of the balloon in terms of time t and use it to determine the volume of the balloon after 8 seconds.
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V+=+4pi%2Ar%5E3%2F3
dV%2Fdt+=+4%2Api%2A%283r%5E2%29%2F3+dr%2Fdt+=+4pi%2Ar%5E2%2Adr%2Fdt
dV%2Fdt+=+4pi%2Ar%5E2%2A7+=+28pi%2Ar%5E2
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Given only the rate of change of the radius, and no initial conditions, only the rate of change in Volume can be determined. Not the volume.