Water Tank Case Study

Main Show Tank Calculation: The main tank has a radius of 70 feet. What is the volume of the quarter-sphered sized 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.

To find the volume of the quarter shaped tank you would have to use the volume of the sphere using the equation V=4/3(3.14)r^3. You would substitute the radius of 70 feet into the equation, V=4/3(3.14)(70*70*70). You would multiply the radius 3 times since it's the radius cubed. Once you use a calculator to solve it and you get the answer 1,436,026.67 feet. That's just the volume of the quarter tank so the find the volume of the main tank you would divide 1,436,026.67 by 4

The bottom of the tank is a curved surface. What is the volume of both tanks if the radius of tank #1 is 15 feet and the height of tank #2 is 120 feet? You must explain your answer using words, and you must show all work and calculations to receive credit.

The first step would be to use the volume of a cyclinder again since the tanks are the shape of a cylinder. The volume of a cyclinder is V=4/3(3.14)r^3. You need to substiute feet and height into the equation resulting in V=4/3(3.14)*15^2*120=4/3(3.14*225*120=63,585 feet. The volume of the whole tank is 65,385 feet. To find the volume of half a cyclinder you would divide the main tanks volume, 65,385 feet by 2 to get 31,792.5 feet. So the volume of the half tanks are 31,792.5

Each dimension will be made 6 times smaller to accommodate the mock-up in the presentation room. How many times smaller than the actual volume is the volume of the mock-up?

The mock is approximately 3 times smaller than the volume.

Using the same information from #5, what percent of change occurred from the actual tank to the mock-up of the tank?

There is a 28,984% change from the mock up tank and the original.

If you were to take a cross section parallel to the base of one of the holding tanks, how would you describe the shape?

I would describe the shape as a sphere because a cross section is the same as the base.

Samples of the tank's water are taken daily to ensure the salt density is correct to maintain aquatic life. The following chart shows the past 2 days' samples:

The salt density of the tank is decreasing daily. If I were in charge of the killer whales tank I would make sure the salinity went back to the normal amount for the whales, I would change it back to original normal salinity from the original