Question

The radius of a cylinder is increasing at \(2\,m/s\) and height is decreasing at \(3\,m/s\). When \(r=3\,m, h=5\,m\), rate of change of volume is:

• A. \(87\pi\, m^3/s\)
• B. \(33\pi\, m^3/s\)
• C. \(27\pi\, m^3/s\)
• D. \(15\pi\, m^3/s\)

Hint:

Use product rule when differentiating volume with respect to time when both radius and height change.

Answer 1

The Correct Option is B