The Volume of a Right Circular Cone of Radius $r$ And Height

question 50

Essay

The volume of a right circular cone of radius $r$ and height $h$ is $V = \frac { \pi } { 3 } r ^ { 2 } h$ . Suppose that the radius and height of the cone are changing with respect to time $t$ .
a. Find a relationship between $\frac { d V } { d t } , \frac { d r } { d t }$ , and $\frac { d h } { d t }$ .
b. At a certain instant of time, the radius and height of the cone are $12 \mathrm { in }$ . and 13 in. and are increasing at the rate of $0.2 \mathrm { in } . / \mathrm { sec }$ and $0.5 \mathrm { in } . / \mathrm { sec }$ , respectively. How fast is the volume of the cone increasing?

Identify the conditions under which online behaviors and social media content are subject to legal scrutiny and discovery.

Comprehend the application of federal and state regulations on e-mail advertising and anti-spam laws.

Understand the concept of heuristics in problem-solving and decision-making.

Recognize and differentiate between various types of heuristics such as availability and representativeness.

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Definitions:

Diversified Portfolio

An investment strategy that involves spreading investments across various financial instruments, industries, and other categories to minimize risk.

Rate of Return

A financial metric used to calculate the percentage profit or loss of an investment relative to its cost.

Beta Risk

A measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole.

Diversified Portfolio

An investment portfolio constructed to spread risk by selecting assets across various classes.