PLEASE HELP PLEASE I NEED IT TODAY

Mathematics

1 answer:

Andrews [41]3 years ago

3 0

Answer:

:) Hope this helps.

Step-by-step explanation:

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Quick calculus question work doesn't have to be shown

Vinil7 [7]

$\bf \textit{volume of a sphere}\\\\
V=\cfrac{4\pi r^3}{3}\implies V=\cfrac{4\pi }{3}r^3
\\\\\\
\cfrac{dV}{dt}=\cfrac{4\pi }{3}\cdot \stackrel{chain~rule}{3r^2\cdot \cfrac{dr}{dt}}\quad 
\begin{cases}
\frac{dr}{dt}=50\\
r=6
\end{cases}\implies \cfrac{dV}{dt}=\cfrac{4\pi }{3}\cdot 3(6)^2\cdot 50\\\\\\ \cfrac{dV}{dt}=\stackrel{\frac{cm^3}{s}}{7200\pi}$