Question

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?

Answer 1

The volume of the scale model of the killer whale stadium main show tank will be 216 times smaller than the actual volume, as volume is proportional to the cube of the linear scale factor.

Step-by-step explanation:

Substituting the relationships between the dimensions into the expression for the mock-up volume, we get:

V_mockup = L_mockup × W_mockup × H_mockup = (L_actual / 6) × (W_actual / 6) × (H_actual / 6)

To determine how many times smaller the volume of the mock-up is compared to the actual volume, we can calculate the ratio of their volumes:

Volume ratio = V_mockup / V_actual

Substituting the expressions for the mock-up and actual volumes, we get:

Volume ratio = [(L_actual / 6) × (W_actual / 6) × (H_actual / 6)] / (L_actual × W_actual × H_actual)

Simplifying the expression, we get:

Volume ratio = 1/216

The volume ratio of 1/216 indicates that the volume of the mock-up is 216 times smaller than the volume of the actual tank. This means that the mock-up tank holds only 1/216th of the water that the actual tank can hold.

Answer 2

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.
density of whale * volume of main show tank


0.000011142* 179503.33=2
If you were to take a cross section parallel to the base of one of the holding tanks, how would you describe the shape?
A sphere
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.

sphere sized tank:
4/3*3.14(70^3) = 1,436,026.67

Main tank:

1,436,026.67/4= 359,007 (rounded)
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?
Mock up is 3x smaller
08.06 Module Eight Activity
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.
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.
84,780/4=21,195
V=3.14*r^2*h
3.14*9^2*72
3.14*5832
=18312 (rounded)
Using the same information from #5, what percent of change occurred from the actual tank to the mock-up of the tank?
21984.4% change
-When the salt decreased, so did the density of the water

-you need to add the amount of salt that the water needs in order to get the water back to normal, then observe the whale's behavior
V=3.14r^2h
3.14 *15^2* 120
706.5*120
=84780 for both tanks because the tanks are half of a cylinder.

...one tank is 42,390
What do you think?