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28 November, 05:43

A hemispherical bowl of radius a contains water to a depth h. Find the volume of the water in the bowl. b. Water runs into a sunken concrete hemispherical bowl of radius 5 m at the rate of 0.2 m cubed divided by sec. How fast is the water level in the bowl rising when the water is 4 m deep?

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  1. 28 November, 07:27
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    a. volume = 2/3*a³

    b. velocity/speed of flow = 0.00127 m/s

    Step-by-step explanation:

    a.) The volume of a sphere is given by 4/3πr³ where r = radius of the sphere.

    The volume of the hemisphere is half the volume of the sphere = 1/2*4/3*πr³

    = 2/3πr³

    With a as the radius, the volume will be

    v = 2/3πa³

    b.) dа ta:

    r = 5 m

    volume flow = 0.2 m³/s

    height = 4 m

    Velocity is calculated by the formula:

    Volume flow = area * velocity

    0.2 = 2πr² * velocity

    0.2/2π (5) ² = 0.00127 m/s Ans
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