The Surface Area of a Sphere Is Given by S $\pi$

question 89

Essay

The surface area of a sphere is given by S = 4 $\pi$ r² where r is the radius of the sphere. The radius is measured to be 6cm with an error of ±0.07cm. Use differentials to estimate the error in the calculated surface area.

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Definitions:

Immanuel Kant

A German philosopher in the 18th century whose work on metaphysics, epistemology, ethics, and aesthetics had a profound impact on various philosophical movements such as the Enlightenment.

Rank Correlation Coefficient

A measure that assesses the degree of association between two ranked variables.

Quantitative Data

Numerical data that can be measured or counted, often used in statistical analysis to quantify behaviors, opinions, or other defined variables.

Linearly Related

A term describing two or more variables that change together in a way that can be represented with a straight line in a graph.