The radius of a right circular cylinder increases at the rate of $0.1 \text{ cm/min}$ and the height decreases at the rate of $0.2 \text{ cm/min}$. The rate of change of the volume of the cylinder in $\text{cm}^3\text{/min}$,when the radius is $2 \text{ cm}$ and the height is $3 \text{ cm}$,is:

  • A
    $-2 \pi \text{ cm}^3\text{/min}$
  • B
    $\frac{-3\pi}{5} \text{ cm}^3\text{/min}$
  • C
    $\frac{-8\pi}{5} \text{ cm}^3\text{/min}$
  • D
    $\frac{2\pi}{5} \text{ cm}^3\text{/min}$

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