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17 February, 07:43

The main show tank has a radius of 60 feet and forms a quarter sphere where the bottom of the pool is spherical and the top of the pool is flat. (Imagine cutting a sphere in half vertically and then cutting it in half horizontally.) What is the volume of the quarter-sphere shaped tank? Round your answer to the nearest whole number. You must explain your answer using words, and you must show all work and calculations to receive credit.

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  1. 17 February, 09:21
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    To obtain the volume we must first know the volume of the full sphere.

    Mathematically, volume of a sphere is given as 4/3 (pi*r^3) where r is the radius of the sphere (60 feet in this case).

    Thus, volume of a quarter sphere shaped tank will be 1/3 (pi*r^3), quarter of a full sphere.

    We simply substitute the value of r to obtain the volume. V = 226,195 ft^3. In other units, V = 6,405 m^3 (1 ft = 0.3048 m so 60 ft = 18.288 m)
  2. 17 February, 11:37
    0
    The volume of quartered sphere tank with a radius of 60 feet will be:

    volume=1/4 (volume of full sphere)

    =1/4 (4/3πr³)

    =1/3πr³

    hence the volume of our sphere will be as follows:

    substituting the values in our formula we get:

    V=1/3*π*60³

    V=882,158.2171 ft³

    Rounding the above to the nearest whole number:

    V=882,158 ft³
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