$\"\"$

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The radius of the spherical balloon is increasing at a rate of $\"\"$ cm/sec.

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(a)

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Consider time taken by the spherical balloon is inflated with radius $\"\"$ is $\"\"$ sec.

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Speed-distance relation:

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$\"\"$

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$\"\"$ .

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The distance inflated by the spherical balloon is

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$\"\"$

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$\"\"$ .

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$\"\"$

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(b)

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Find $\"\"$ .

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Volume of the sphere is $\"\"$ .

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So $\"\"$ .

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The volume of the balloon $\"\"$ as the function of the radius $\"\"$ is

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$\"\"$

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$\"\"$ ( Since $\"\"$ )

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$\"\"$

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$\"\"$ .

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$\"\"$

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(a) $\"\"$ .

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(b) The volume of the balloon as the function of time $\"\"$ is $\"\"$ .