Question

Oil from a conical funnel is dripping at the rate of \(5\ \text{cm}^3/\text{s}\). If the radius and height of the funnel are 10 cm and 20 cm respectively, then the rate at which the oil level drops when it is 5 cm from the top is

• A. \( \frac{8}{45\pi} \) cm/s
• B. \( -\frac{8}{45\pi} \) cm/s
• C. \( -\frac{4}{45\pi} \) cm/s
• D. \( \frac{4}{45\pi} \) cm/s

Hint:

In related rates problems involving cones, first use similarity of triangles to express \(r\) in terms of \(h\), then differentiate volume with respect to time.

Answer 1

The Correct Option is D