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Stone dropped in a lake, circular wave spreading: rate the enclosed area grows

The same question, asked 3 times: 3 May 2023 S1*, 19 Apr 2025 S1*, 14 May 2026 S2. Every wording below, oldest first.

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  1. Question 1

    3 May 2023 S1

    118
    A stone is dropped into a quiet lake and waves move in circles at speed of 8 cm/sec. At the instant when the radius of the circular wave is 12 cm, how fast is the enclosed area increasing?

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  2. Question 2

    19 Apr 2025 S1

    139
    By dropping a stone in a quiet lake, a wave in the form of circle is generated. The radius of the circular wave increases at the rate of 2.1 cm/sec2.1\text{ }cm/sec. Then the rate of increase of the enclosed circular region, when the radius of the circular wave is 10 cm , is (Given π=227\pi=\frac{22}{7} )

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  3. Question 3

    14 May 2026 S2

    77
    A stone is dropped into a quiet lake and waves move in circles at the speed of 7 cm s−17\ \mathrm{cm\,s^{-1}}. At the instant when the radius of circular wave is 55 cm, the enclosed area is increasing at the rate -------- cm2 s−1\mathrm{cm^2\,s^{-1}}

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