Question

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

• A. \( -2\pi \)
• B. \( -\frac{8\pi}{5} \)
• C. \( \frac{3\pi}{5} \)
• D. \( 2\pi \)

Hint:

Use the related rates method to differentiate and find the rate of change of volume for a cylinder.

Answer 1

The Correct Option is B

The volume of a cylinder is \( V = \pi r^2 h \). Differentiate the equation with respect to time and substitute the given rates of change to get the rate of change of volume.
Final Answer: \[ \boxed{-\frac{8\pi}{5}} \]