Solve the Problem $2.19 \mathrm {~mm} ^ { 3 } / \mathrm { mm }$

question 321

Multiple Choice

Solve the problem.
-A cubic salt crystal expands by accumulation on all sides. As it expands outward find the rate of change of its volume with respect to the length of an edge when the edge is 0.27 mm.

• A) \(2.19 \mathrm {~mm} ^ { 3 } / \mathrm { mm }\)
• B) \(21.87 \mathrm {~mm} ^ { 3 } / \mathrm { mm }\)
• C) \(0.2187 \mathrm {~mm} ^ { 3 } / \mathrm { mm }\)
• D) \(0.06 \mathrm {~mm} ^ { 3 } / \mathrm { mm }\)

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Definitions:

Standard Deviation

An indicator of the spread of a dataset relative to its mean, used to quantify the degree to which individual data points differ from the average.

Monthly Production

The total output or production of a manufacturing process or facility in a single month.

Probability Distribution

Describes how the values of a random variable are distributed, showing the probabilities of different outcomes occurring.

Variance

A measure of the spread or dispersion of a set of values, calculated as the average of the squared deviations from the mean.