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Main Show Tank Calculation:1. 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:2. 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 acurved 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 youranswer using words, and you must show all work and calculations to receive creditDensity Calculation:3. 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 themaximum number of killer whales allowed in the main show tank at any given time? You must explain your answer using words, and you mustshow all work and calculations to receive credit.

Main Show Tank Calculation:1. The main tank has a radius of 70 feet. What is the volume-example-1

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\begin{gathered} 1. \\ \text{Radius}=70ft \\ V=(4)/(3)\pi^{}r^3 \\ To\text{ find the volume of the quarter-sphere sized, we n}eed\text{ to divide the } \\ \text{volume of the sphere by 4} \\ V=(4)/(3)\pi^{}r^3\cdot(1)/(4) \\ V=(\pi r^3)/(3) \\ V=(\pi(70ft)^3)/(3) \\ V=359,189ft^3 \\ \text{The volume of }To\text{ find the volume of the quarter-sphere sized tank is} \\ 359,189ft^3 \\ \\ 2. \\ Two\text{ cylinders are congruent when they have the same side}s \\ r=15ft \\ h=120ft \\ V=\pi r^2h \\ V=\pi(15^2\text{)(120)} \\ V=84,823ft^3 \\ \text{The volume of both cylinders is }84,823ft^3 \\ \\ 3. \\ density=\text{ }0.000011142\text{ }killer\text{ }whales/ft^3 \\ \text{number of killer whales=?} \\ V=(4)/(3)\pi^{}r^3 \\ r=70ft \\ V=(4)/(3)\pi^{}(70ft)^3 \\ V=1,436,756ft^3 \\ To\text{ find the numbers of killer whales we have to }multiply\text{ the density } \\ \text{and the volume} \\ \text{number of killer whales=density}\cdot\text{Volume} \\ \text{number of killer whales=( }0.000011142\text{ }killer\text{ }whales/ft^3\text{)}\cdot(1,436,756ft^3) \\ \text{number of killer whales=16} \\ \text{The maximun number of killer whales is 16.} \\ \\ 4. \\ Each\text{ dimension six times smaller} \\ r=(70ft)/(6) \\ r=11.7ft \\ V=(4)/(3)\pi(11.7ft)^3 \\ V=6709ft^3 \\ \text{times smaller=}(1,436,756ft^3)/(6709ft^3) \\ \text{times smaller=214} \\ \text{The volume of the mock-up is 214 times }smaller\text{ than the actual volume} \\ \\ 5. \\ \text{ percentage}=\frac{Volume\text{ of the actual tank }}{\text{volume }mock-up\text{ }tank}\cdot100 \\ \text{ percentage}=(1,436,756ft^3)/(6709ft^3)\cdot100 \\ \text{percentage}=21400 \\ \text{The volume of the actual tank is 21400\% }of\text{ the mock-up of the tank} \\ \\ 6.\text{ } \\ The\text{ shape would be as circle} \end{gathered}

Main Show Tank Calculation:1. The main tank has a radius of 70 feet. What is the volume-example-1
Main Show Tank Calculation:1. The main tank has a radius of 70 feet. What is the volume-example-2
Main Show Tank Calculation:1. The main tank has a radius of 70 feet. What is the volume-example-3
Main Show Tank Calculation:1. The main tank has a radius of 70 feet. What is the volume-example-4
Main Show Tank Calculation:1. The main tank has a radius of 70 feet. What is the volume-example-5
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