A Wooden Beam Has a Rectangular Cross Section of Height $S = k w h ^ { 2 },$

question 31

Multiple Choice

A wooden beam has a rectangular cross section of height h and width w (see figure) . The strength S of the beam is directly proportional to the width and the square of the height. What are the dimensions of the strongest beam that can be cut from a round log of diameter d = 23 inches? Round your answers to two decimal places. [Hint: $S = k w h ^ { 2 },$ where $k > 0$ is the proportionality constant.]

• A)w = 13.28 inches and h = 18.78 inches
• B)w = 7.67 inches and h = 21.68 inches
• C)w = 19.92 inches and h = 11.50 inches
• D)w = 16.26 inches and h = 16.27 inches
• E)w = 18.78 inches and h = 13.28 inches

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Definitions:

Spongy Bone

Consists of a network of thin strands of bone; provides mechanical strength.

Compact Bone

Dense, hard bone tissue found mainly near the surfaces of a bone.

Osteons

Structural units found in compact bone, consisting of a central canal surrounded by concentric rings of calcified matrix.

Bone Marrow

The soft, cellular tissue that fills the internal spaces of bones; red bone marrow in certain bones produces blood cells.