The Volume of a Right Circular Cone of Radius

question 132

Essay

The volume of a right circular cone of radius and height is Suppose that the radius and height of the cone are changing with respect to time a.Find a relationship between b.At a certain instant of time, the radius and height of the cone are 12 in.and 13 in.and are increasing at the rate of 0.2 in./sec and 0.5 in./sec, respectively.How fast is the volume of the cone increasing?

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Definitions:

Central Chemoreceptors

Brainstem neurons that detect changes in the pH of cerebrospinal fluid and help regulate ventilation rate.

Peripheral Chemoreceptors

Sensory receptors located in the carotid bodies and aortic bodies that detect changes in the chemical composition of the blood, primarily oxygen, carbon dioxide, and pH levels.

Irritant Receptors

Sensory nerve endings that respond to chemical, mechanical, or thermal stimuli by initiating the reflex actions such as coughing or sneezing.

Expiratory Muscles

Muscles involved in the process of expelling air out of the lungs, such as the internal intercostal muscles and abdominal muscles.