[tex]\begin{gathered} 1. \\ \text{Radius}=70ft \\ V=\frac{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=\frac{4}{3}\pi^{}r^3\cdot\frac{1}{4} \\ V=\frac{\pi r^3}{3} \\ V=\frac{\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=\frac{4}{3}\pi^{}r^3 \\ r=70ft \\ V=\frac{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=\frac{70ft}{6} \\ r=11.7ft \\ V=\frac{4}{3}\pi(11.7ft)^3 \\ V=6709ft^3 \\ \text{times smaller=}\frac{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}=\frac{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}[/tex]
