A Coffee Filter Is in the Shape of a Cone $\sqrt{h}$

question 21

Multiple Choice

A coffee filter is in the shape of a cone, as shown below.Suppose that when it is filled with water to a height h cm, the rate at which coffee flows out the hole at the bottom is given by Volume of coffee which flows out per second = $\sqrt{h}$ cm³ / sec. Approximately how many cubic centimeters are in the "slice" of coffee lying below h + $\Delta$ h and above h?

• A) \(\pi h^{3} \Delta h\)
• B) \(\pi h \Delta h\)
• C) \(\pi h^{2} \Delta h\)
• D) \(\pi h^{3 / 2} \Delta h\)

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Definitions:

Devil's Advocate

A role adopted by an individual in discussions or decision-making processes to present alternative or opposing arguments, aiming to challenge assumptions and promote critical thinking.

Stimulates Controversy

Provokes debate or disagreement on a specific topic due to differing opinions, beliefs, or interests among individuals or groups.

Diffusion Of Responsibility

The ability of group members to share the burden of the negative consequences of a poor decision.

Risky Shifts

Risky shift phenomenon observes that groups tend to make decisions that are riskier than the individual decisions of group members due to the diffusion of responsibility and group influence.