Part 3:
The volume of a sphere is given by:
[tex]V= \frac{4}{3} \pi r^3[/tex]
Given that 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.
The volume of the quarter-sphere shaped tank is given by:
[tex]V= \frac{1}{4} \cdot \frac{4}{3} \pi (60)^2=1200\pi\approx3770\, cubic\, ft.[/tex]
Part 2:
The volume of a cylinder is given by:
[tex]V=\pi r^2h[/tex]
Given that the
holding tanks are in the shape of a cylinder that
has been cut in half vertically.
The volume of the tanks if tank #1 have a radius of 30 feet and the height of tank #2 is 110 feet.
Since both tanks are congruent, then the radius and the height of both matches are equal.
Therefore the volume of the half-tanks is given by:
[tex]V= \frac{1}{2} \pi(30)^2\times110=49,500\pi\approx155,509\, cubic\, ft[/tex]
Part 3:
The volume of a the tank is given by:
[tex]V=LWH[/tex]
Given that the dimensions of the mock-uk is 1/8 the original dimensions, then the volume of the mock up is given by:
[tex]Volume= \frac{L}{8} \times \frac{W}{8} \times \frac{H}{8} = \frac{1}{512} LWH[/tex]
Therefore, the volume of the mock-up is 1/512 the volume of the original tank.
