Gravel Is Being Dumped from a Conveyor Belt at a Rate

question 130

Multiple Choice

Gravel is being dumped from a conveyor belt at a rate of $34 \mathrm { ft } / \mathrm { min }$ and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is $13 \mathrm { ft }$ high? Round the result to the nearest hundredth.

• A) \(\quad 0.6 \mathrm { ft } / \mathrm { min }\)
• B) \(0.26 \mathrm { ft } / \mathrm { min }\)
• C) \(0.14 \mathrm { ft } / \mathrm { min }\)
• D) \(\quad 0.27 \mathrm { ft } / \mathrm { min }\)
• E) \(1.24 \mathrm { ft } / \mathrm { min }\)