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.

r = 70ft

V=4/3(πr^3)

STEPS

1.V=4/3(π70^3)

2.V=4/3(π343000)

3.V=1372000π/3

4.V=1436755/4

5. = 359189

Take the radius and cube it, then

multiply the result by 4 and π. Divide

it all by 3 and divide by 4 (to find the quarter

of the sphere.) The result is 359189 feet cubed.

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?

r=15 h= 120 V=πr^2(h)

STEPS

1.V=π15^2(120)

2.V=π205(120)

3.V=π(27000)

4.V=84823/2

5. = 42411.5

The tanks are split in half evenly, so you solve for the volume of a normal cylinder. Square the radius and multiply it by the height and π. Divide the result by 2 to get the volume of one tank. The result is 42411.5 feet cubed.

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?

V=359189 cubic ft D=m/v

STEPS

1.0.000011142 = m/359189

2.(0.000011142 x 359189) = m

3.m = 4

The formula for density is mass divided by volume. In this problem we have the density and volume. With this we can find the mass. Fill in the information already known, then cross multiply so that m is isolated on one side. The result if 0.000011142 x 359189 is 4. 4 killer whales can be in the main tank at a time.

Reflections

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?

The mock-up is 3 times smaller than

the original holding tank.

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

There is actually a 28984.44% change between

the mock-up tank and the original.

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?

I would say the shape is a sphere.

8. 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?

The information in the chart is showing that salt density in the water is lowering. At 1st it isn't much of a problem, but by the second day a great amount is missing. I think that too much water is also being added into the tank. I would bring the density back to normal, adding more salt, and install a device to warn when the salt density is getting low.

**Thanks for Watching!**