$\"\"$

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(a)

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The surface area of the snowball decreases at a rate of $\"\"$ cm²/min.

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(b)

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The rate at which diameter decreases when the diameter is 10 cm.

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(c)

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Diagram of the situation at any time $\"\"$ .

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$\"\"$

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The diameter of the snow ball is considered as $\"\"$ .

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$\"\"$

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(d)

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Surface area of the sphere is $\"\"$ .

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Radius is half of the diameter $\"\"$ .

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Rewrite the surface area in terms of diameter $\"\"$ .

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Therefore, $\"\"$

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$\"\"$

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(e)

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Consider $\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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The surface area of the snowball decreases at a rate of $\"\"$ cm²/min.

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Thus, $\"\"$ .

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The rate at which diameter decreases when the diameter is 10 cm.

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Thus, $\"\"$ cm.

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Substitute $\"\"$ and $\"\"$ in equation (1).

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$\"\"$

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The rate at which diameter decreases when the diameter is 10 cm is $\"\"$ cm/min.

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$\"\"$

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(a)

\

The surface area of the snowball decreases at a rate of $\"\"$ cm²/min.

\

(b)

\

The rate at which diameter decreases when the diameter is 10 cm.

\

(c)

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Diagram of the situation at any time $\"\"$ :

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$\"\"$

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(d)

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$\"\"$ .

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(e)

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The rate at which diameter decreases when the diameter is 10 cm is $\"\"$ cm/min.