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Sphere whose volume changes at a rate proportional to its surface area

This type of question, asked 4 times: 10 May 2023 S2, 9 May 2024 S1, 13 Apr 2026 S1, 15 Apr 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    10 May 2023 S2

    140
    A spherical rain drop evaporates at a rate proportional to its surface area. If initially its radius is 3 mm and after 1 second it is reduced to 2 mm, then at any time t its radius is (where 0≤t<30 \leq t < 3)

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  2. Question 2

    9 May 2024 S1

    145
    A spherical raindrop evaporates at a rate proportional to its surface area. If originally its radius is 3 mm and 1 hour later it reduces to 2 mm, then the expression for the radius R of the raindrop at any time tt is

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  3. Question 3

    13 Apr 2026 S1

    85
    A spherical balloon expands at a rate proportional to its surface area. Initially its radius is 2 cm and 5 minutes later it increases upto 7 cm, then surface area of spherical balloon after 12 minutes will be

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  4. Question 4

    15 Apr 2026 S2

    77
    A spherical mothball has initial radius 3 cm. Due to evaporation, the radius of the ball reduces to 1 cm in 4 months. In how many months would the mothball evaporate completely if the volume is lost at a rate proportional to the surface area ?

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