16 August, 01:43

# 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. 16 August, 02:00
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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. 16 August, 02:03
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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