Question
The radius of an air bubble is increasing at the rate of . At what rate is the volume of the bubble increasing when the radius is ?
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The air bubble is in the shape of a sphere.
Now, the volume of an air bubble with radius is given by,
The rate of change of volume with respect to time is given by,
It is given that cm/s
Therefore, when cm,
Hence, the rate at which the volume of the bubble increases is .
Now, the volume of an air bubble with radius is given by,
The rate of change of volume with respect to time is given by,
It is given that cm/s
Therefore, when cm,
Hence, the rate at which the volume of the bubble increases is .
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Question Text | The radius of an air bubble is increasing at the rate of . At what rate is the volume of the bubble increasing when the radius is ? |
Answer Type | Text solution:1 |
Upvotes | 150 |