CALCULATIONS

1)Main Show Tank Calculation:

The main tank has a radius of 70 feet. What is the volume of the quarter-sphere 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.

　

First you need to find the volume of the sphere. The formula for the volume of a sphere:

v=4/3 pi r^3

V= 4/3(3.14)(343000) = 1,436,026.67


divide the volume of the sphere by 4.
1,436,026.67 / 4 = 359,006.6675.


　

2) Holding Tank Calculations:

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.

You would use the formula for cylinders.

V = pi r^2 h
V = 3.14 (225) (120)
V = 84,780


84,780 ft is the volume of the whole tank. Now what we want to do is cut this is half:

84,780/2= 42,390

42,390 is your final answer for both tanks.

　

3) 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.

　

　

To find the maximum number of killer whales allowed we have to multiply the density by the volume of the main tank.

density = mass / volume

0.000011142 = x/359,006.6675

then multiply both sides by the volume.

mass= 4

The maximum number of whales would be 4.

REFLECTIONS

Answer the following questions:

You must show all steps and provide any evidence needed in your solution to receive full credit.

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?

  If all the dimensions scale by a factor of k , then the volume scales by a factor of k^3k 3

If all linear dimensions are 6 times smaller then that means we take 6 to the third power which is 216. The mock up would be 216 times smaller.

Using the information from #4, answer the following question by filling in the blank: The volume of the actual tank is 21,600% of the mock-up of the tank

216*100=21,600

 

 

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