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Rate at which the water level rises or falls in a cylinder, cone or bowl

This type of question, asked 5 times: 10 May 2023 S1, 16 May 2023 S2, 9 May 2024 S2, 13 May 2024 S2, 13 May 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    10 May 2023 S1

    110
    Water is running in a hemispherical bowl of radius 180 cm at the rate of 108 cubic decimeters per minute. How fast the water level is rising when depth of the water level in the bowl is 120 cm? (1 decimeter = 10 cm)

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  2. Question 2

    16 May 2023 S2

    111
    Water is being poured at the rate of 36 m3/min\text{m}^3/\text{min} into a cylindrical vessel, whose circular base is of radius 3 meters. Then the water level in the cylinder is rising at the rate of

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  3. Question 3

    9 May 2024 S2

    135
    A water tank has a shape of inverted right circular cone whose semi-vertical angle is tan⁡−1 ⁣12\tan^{-1}\!\frac{1}{2}. Water is poured into it at constant rate of 5 cubic meter/minute. The rate in meter/minute at which level of water is rising, at the instant when depth of water in the tank is 10 m is

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  4. Question 4

    13 May 2024 S2

    133
    Water is running in a hemispherical bowl of radius 180 cm at the rate of 108 cubic decimeters per minute. How fast the water level is rising when depth of the water level in the bowl is 120 cm? (1 decimeter =10=10 cm)

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  5. Question 5

    13 May 2026 S2

    76
    A water tank in the house of an inverted cone is being emptied at the rate of 22 cubic feet per second. The height of the cone is 88 feet and the radius is 44 feet, then the rate of change of the water level when the depth is 66 feet.

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