A Rectangular Beam Will Be Cut from a Cylindrical Log $r = 40$

question 17

Multiple Choice

A rectangular beam will be cut from a cylindrical log of radius $r = 40$ inches. Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log.

• A) \(\sqrt { 3 }\) in, 80 in
• B) \(\frac { 80 } { \sqrt { 3 } }\) in, \(80 \sqrt { \frac { 2 } { 3 } }\) in
• C) \(\frac { 80 } { \sqrt { 3 } }\) in, \(\frac { 80 } { \sqrt { 3 } }\) in
• D) \(80 \sqrt { \frac { 2 } { 3 } }\) in, \(80 \sqrt { \frac { 2 } { 3 } }\) in
• E) 80 in, \(\sqrt { \frac { 2 } { 3 } }\) in

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Definitions:

Sample Proportion

The ratio of the number of times an event occurs to the total number of observations or trials in the sample.

Standard Error

Standard error measures the accuracy with which a sample distribution represents a population by quantifying the variability of the sample mean.

Population Proportion

The fraction or percentage of a population possessing a particular characteristic.

Sample Size

The number of observations or units chosen from a population to participate in a study.