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

question 49

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) \(\sqrt { 3 } \mathrm { in } , 80 \mathrm { in }\)
• 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:

M

A symbol often representing money supply in economic discussions, including various measures like M1, M2, and M3.

Q

Quantity, frequently used in economic equations and discussions to denote the amount of goods produced or consumed.

PQ

The product of price (P) and quantity (Q), often used in economics to calculate total revenue or expenditure.

P

Typically refers to "Price" in economic models, representing the monetary value assigned to a good or service in the market.