The Volume $V = \pi r ^ { 2 } h$

question 80

Short Answer

The volume $V = \pi r ^ { 2 } h$ of a right circular cylinder is to be calculated from measured values of r and h.Suppose r is measured with an error of no more than 2.5% and h with an error of no more than 1%.Using differentials, estimate the percentage error in the calculation of V.
(In general, in measuring a quantity Q, the percentage error is dQ/Q.)

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Definitions:

Immune Response

The body's defensive reaction to foreign substances or microorganisms, including both specific and nonspecific mechanisms.

Eosinophils

A type of white blood cell that is involved in the body’s immune response, particularly in fighting off certain parasitic infections and in allergic reactions.

Phagocytosis

The ingestion of particles by a cell or phagocyte, playing a crucial role in the immune response by clearing pathogens.

Antigen-Antibody Complexes

Molecular structures formed when antibodies bind to their specific antigens, often triggering an immune response.