The surface area of a spherical bubble is increasing at the rate of 2 `c m^2//s` . When the radius of the bubble is 6cm, at what rate is the volume of the bubble increasing?

Explanation

`S=4 pi r^{2} `
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Rightarrow frac{d S}{d t}=8 pi r frac{d r}{d t} `
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Rightarrow frac{d r}{d t}=frac{1}{8 pi r} frac{d S}{d t} `
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Rightarrow frac{d r}{d t}=frac{2}{8 pi times 6} `
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Rightarrow frac{d r}{d t}=frac{1}{24 pi} `cm / sec


Now,


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