**08.06 Module Eight Activity**

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

6.) Use the same information from #5, what percent of change occurred from the actual tank to the mock-up of the tank?

Design

4.) The stadium is in need of a medical pool to attend to injured or sick whales. The pool will be located adjacent to the holding tanks. Your job is to design a medical pool using a 3-dimensional polyhedral shape you learned about in this module. For safety reasons, the tank can be no more than one-fourth the volume of a holding tank. You will need to submit a 2-dimensional drawing, the dimensions, the volume of your pool, and proof that the pool's volume is no more than one-fourth the volume of a holding tank to your instructor.

5.) The theme park company is building a scale model of the killer whale stadium main show tank for an investor's presentation. 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?

Image by goodtextures: http://fav.me/d2he3r8

A theme park company is opening a marine-inspired park in your city. They are in the process of designing the theater where a killer whale show will take place. The following design is already under construction and will house the whales that perform in the show:

Main Show Tank Calculation:

1.) 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.

Holding Tank Calculations:

Density Calculation:

In step 1, you found the volume (in cubic feet) of the main tank. If the maximum density of killer whales per cubic foot is 0.000011142, what is the maximum number of killer whales allowed in the main show tank at any given time? You must explain your answer using words, and you must show all work and calculations to receive credit.

8.) 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 day's samples:. Describe the information in the chart using words. What do you think the information shown means? If you were in charge of the killer whale tank, what action might you take after seeing the samples shown above?

Step 1:

Calculations

~To find the volume of a quarter-sphered sized tank, the formula of the volume of a sphere must be used. After finding the volume of a sphere which is 1,436,026.667 feet, since the main tank is a quarter of a sphere, divide the volume of the sphere by 4 to get the volume of just a quarter - sphere The volume of a quarter-sphered sized tank is 359,006.668 feet.

The volume of the quarter-sphered size main tank is 359,007 cubic feet.

2.) The holding tanks are congruent in size and both are in the shape of a cylinder that has been cut in half vertically. 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.

Since both tanks are congruent in size and both are in the shape of a cylinder that has been cut in half vertically, both tanks must have the same radius and the same height. To find the volume of both tanks,use the formula of the volume of a cylinder . The volume of a whole cylinder is 84,780 feet. But like said before, both tanks have been cut in half vertically, meaning the volume found was the volume of a whole cylinder. To find the volume of the tanks, which are half of a cylinder, divide the volume of the whole cylinder by 2.

The volume of each tank is 42,390 cubic feet. When the volume of each tank is added together, they add up to have a volume of 84,780 cubic feet.

To find the maximum number of killer whales allowed in the main show tank at any given time, multiply the density of the killer whales ( 0.000011142 per cubic foot) by the volume of the main tank (359,007). After the multiplication, the result is 4.00005599, rounded up to the nearest whole number is 4. So 4 killer whales are allowed in the main show tank at any given time.

Step 2:

Design

~

Since the medical pool is located adjacent to the holding tanks and the medical pool can be no more than one-fourth the volume of a holding tank, then i divided the volume of one of the holding tanks which is 42,390 cubic feet by four and the result was 10,597.5. The medical pool can have a volume of no more than 10,597.5 cubic feet. As of this, the medical pool will be in the shape of a cylinder that has been cut in half vertically just like the holding tanks. The radius of the medical pool is 7 feet and the height is 120 feet. To find the volume of the medical pool, use the formula of the volume of a cylinder. The volume of the cylinder pool is 18,463.2. Now since the pool is in the shape of half of a cylinder, divide the volume of the whole cylinder by 2 to find the volume of only half of the cylinder.

The medical pool has a volume of 9,231.6 cubic feet.

4 killer whales are allowed in the main show tank at any given time

Reflections

The scale factor between these two figures is 6, so the ratio of the volumes can be found by cubing the scale factor. Meaning the scale factor of 6 when cubed equals 216. If each dimension will be 6 times smaller to accommodate the mock-up in the presentation room, the volume of the mock up would be about 3 (216) times smaller than the actual volume. It is 1/216 of the actual volume.

Since the mock- up of the tank is 216 times smaller (1/216) we multiply that by 100 so it would be 0.462963 . Turning that into a percentage, move the decimal point. So the percent of change that occurred is 46%.

The holding tanks are are in the shape of a cylinder that has been cut in half vertically. If I were to take the cross section parallel to the base of the holding tanks, I would describe the shape of the cross section as a semi-circle (half of a circle). The shape of the cross section of a cylinder is a circle, so since the holding tanks are in the shape of a cylinder except cut in half, the shape made by the cross section must be a semi circle.

Based on the chart, I can identify that as the days passed, the grams of salt per liter of seawater went down as well as the approximate density. I think the information shown shows the data after an experiment that is being observed. If i was in charge of the killer whale tank, the action that I would take after seeing the samples shown above is that add the water that is missing but keep decreasing the grams of salt per liter of seawater each day and observe and record the reaction of the killer whales.