Question

HELP PLEASE 25 POINTS CALC

Answer 1

`18\pi\: cm^3/s`

Explanation:

`V= \frac {4}{3}\pi r^3\\\\</p><p>`

Differentiating with respect to t on both sides:

`(dV)/(dt) = \frac {4}{3}\pi* 3r^2(dr)/(dt) \\\\</p><p> (dV)/(dt) =4\pi r^2(dr)/(dt) .. (1)\\\\</p><p>Plug \:(dr)/(dt) = (1)/(2)\:\: \& \: \: r = 3\: in \: equation \: (1)\\\\</p><p>(dV)/(dt) =4\pi (3)^2* (1)/(2)\\\\</p><p>(dV)/(dt) =4\pi* 9* (1)/(2)\\\\</p><p>\huge \purple {\boxed{(dV)/(dt) =18\pi\: cm^3/s}} \\`