6.6millimeters of rain fall into a rectangular roof. 8meters long and 6 meters wide. The rainwater drains into a cylindrical barrel of diame

Question

6.6millimeters of rain fall into a rectangular roof. 8meters long and 6 meters wide. The rainwater drains into a cylindrical barrel of diameter 60centimeters. How far does the water level rise in the barrel​

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Ladonna 5 years 2021-09-02T13:11:57+00:00 1 Answers 14 views 0

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  1. trungdung22
    0
    2021-09-02T13:13:55+00:00
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    Answer:

    1.12 meters

    Step-by-step explanation:

    this is the same as filing a box with the same ground area 6.6 millimeters high and then drain it at once into the barrel.

    so, the volume of the box filling is (1 m = 1000 mm)

    Vb = 8000 × 6000 × 6.6

    now, this is then also the volume of the cylinder when filling it up with everything inside the box.

    and the general volume of a cylinder is (as for the box) ground area times height.

    just here the ground area is a circle with the diameter of 60 cm and therefore the radius of 60/2 = 30 cm.

    1 cm = 10 mm => r = 300 mm

    the area of a circle is

    Ac = pi×r²

    =>

    Vc = pi×r²×h(eight) = pi×300²×h

    and that is also the value of Vb.

    Vc = Vb = pi×90000×h

    h = Vb / (pi×90000) = 8000×6000×6.6/(pi×90000) =

    = 800×6×6.6/(pi×9) = 800×2×2.2/pi = 800×4.4/pi =

    = 1120.45 mm = 1.12 m

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