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.