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Furkat [3]
3 years ago
9

The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 m

m
Mathematics
1 answer:
jeka943 years ago
4 0

9514 1404 393

Answer:

  8000π mm^3/s ≈ 25,133 mm^3/s

Step-by-step explanation:

The rate of change of volume is found by differentiating the volume formula with respect to time.

  V = 4/3πr^3

  V' = 4πr^2·r'

For the given numbers, this is ...

  V' = 4π(20 mm)^2·(5 mm/s) = 8000π mm^3/s ≈ 25,133 mm^3/s

_____

<em>Additional comment</em>

By comparing the derivative to the area formula for a sphere, you see that the rate of change of volume is the product of the area and the rate of change of radius. This sort of relationship will be seen for a number of different shapes.

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Stephen spends 10% of his salary on food, 15% of it on transportation, and saves the remaining 2000. what is his salary?
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\frac{sinx}{1-cos x}     =         cosecx  +  cot x

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 \frac{cosx}{sinx}   =       cot x

                                     

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