Question

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.

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)

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