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# Calc Help

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The volume of a cylinder of height 11 inches and radius r inches is given by the formula V=11πr2.

Suppose that the radius is expanding at a rate of 0.6 inches per second. How fast is the volume changing when the radius is 2.3 inches? Use at least 5 decimal places in your answer.  ____???cubic inches per second

Jun 10, 2020

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The volume of a cylinder of height 11 inches and radius r inches is given by the formula V=11πr2.

Suppose that the radius is expanding at a rate of 0.6 inches per second. How fast is the volume changing when the radius is 2.3 inches? Use at least 5 decimal places in your answer.  ____???cubic inches per second

$$V=11\pi r^2\\ \frac{dV}{dR}=22\pi r$$

$$\frac{dr}{dt}=0.6$$

$$\frac{dV}{dt}=\frac{dV}{dr}\times \frac{dr}{dt}\\ \frac{dV}{dt}=22\pi r\times 0.6\\ \frac{dV}{dt}=13.2\pi r\\ When\;\;r=2.3\; inches\\ \frac{dV}{dt}=13.2\pi *2.3\\ etc$$

LaTex:

V=11\pi r^2\\
\frac{dV}{dR}=22\pi r

\frac{dr}{dt}=0.6

\frac{dV}{dt}=\frac{dV}{dr}\times \frac{dr}{dt}\\
\frac{dV}{dt}=22\pi r\times 0.6\\
\frac{dV}{dt}=13.2\pi r\\
When\;\;r=2.3\; inches\\
\frac{dV}{dt}=13.2\pi *2.3\\
etc

Jun 10, 2020