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.

Question

Mathematics

Linda Morton

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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Answers (2)

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Savannah Henry · Answer 1

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)

Anton Rowe · Answer 2

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