math project, help! WILL FAN AND GIVE MEDAL

A theme park company is opening a marine-inspired park in your city. They are in the process of designing the theatre 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:

A diagram of a show stadium is shown. The main show tank appears to be a semi-circle, while the two holding tanks appear to be rectangular in shape.

Step 1: Calculations

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.

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.

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.

Step 2: 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?
Using the information from #4, answer the following question by filling in the blank: The volume of the actual tank is ____% of the mock-up of the tank
If you were to take a cross section parallel to the base of one of the holding tanks, how would you describe the shape?

Question

math project, help! WILL FAN AND GIVE MEDAL

A theme park company is opening a marine-inspired park in your city. They are in the process of designing the theatre 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:

A diagram of a show stadium is shown. The main show tank appears to be a semi-circle, while the two holding tanks appear to be rectangular in shape.

Step 1: Calculations

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.

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.

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.

Step 2: 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?
Using the information from #4, answer the following question by filling in the blank: The volume of the actual tank is ____% of the mock-up of the tank
If you were to take a cross section parallel to the base of one of the holding tanks, how would you describe the shape?

math_genius12345 · Answer

attachment

math_genius12345 · Answer

so I should just start by finding the volume of the main tank, right?

lord_box · Answer

Yes. What would be the volume formula for a quarter sphere?

math_genius12345 · Answer

this is the formula I found but it looks super complicated

lord_box · Answer

Hm, I don't think that's it. You know the volume formula for a sphere?

math_genius12345 · Answer

359189 is the number I got for cubic feet in the main tank

math_genius12345 · Answer

1436755.0402417321077235822406198 for the full sphere and 359188.76006043302693089556015496 divided by four

lord_box · Answer

That looks to be correct.

math_genius12345 · Answer

For the third part, I got
x whales ≤ 4.002083838
So four whales in the tank at one time

math_genius12345 · Answer

Does anyone know of a program where I can build a 3D model of this? I think it might help me.

lord_box · Answer

I agree with your step 3.

math_genius12345 · Answer

great

lord_box · Answer

tinkercad might help you with 3D modeling

lord_box · Answer

Holding Tank Calculations: It describes half of a cylinder. It tells you the two tanks are congruent, so their measurements should be the same. 15 radius and 120 height. The equation for cylinder area is $$\pi*r^2*h$$

math_genius12345 · Answer

V=(3.14)R^2H
V=(3.14)(15)^2(120)
V=(3.14)(225)(120)
V=84,780

lord_box · Answer

That would be the volume of both combined.

math_genius12345 · Answer

Should I divide by two?

lord_box · Answer

I suppose the "volume of both tanks" means both of them. But it could mean either one, not sure.