Question

A cylindrical tank has a height of 12 feet and a diameter of 16 feet. Jane fills the tank with water at a rate of 6 cubic feet per minute. Calculate how long it would take Jane to fill the tank without overflowing it. Explain your reasoning. Round as needed.

Answer 1

if the diameter is 16 feet, then the radius for the tank will have to be half that,


`\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h\quad \begin{cases} r=radius\\ h=height\\ -----\\ r=8\\ h=12 \end{cases}\implies V=\pi \cdot 8^2\cdot 12\implies V=\stackrel{ft^3}{768\pi}`

now, that's how many ft³ of water the tank can hold, since she is filling it up at a rate of 6 ft³ per minute, namely in 1 minute 6 ft³ have gone in, then it'll be

768π/6 how many minutes it'll take.

namely, how many times does 6 go into 768π? well, 768π/6.