# Find the volume and the total area of the largest cube of wood that can be cut from a log of circular cross section whose radius is 12.7 in.

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by almegen

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by almegen

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To solve for the edge, find the diagonal of the square given the radius (12.7 inches) of the circular cross section.

Diagonal of the square = Diameter of the cirle (2 × radius)

=

Solve for

diagonal = hyptonuse = 25.4 inches

(25.4 in)² = a² + a²

2a² = (25.4 in)²

=

a =

a =

a = in

VOLUME OF INSCRIBED CUBE:

Volume = a³

Volume = (12.7 )³

Volume = 2,048.38 (2) in³

Volume ≈ 4,096.76 (1.4142) in³

SURFACE AREA OF CUBE:

SA = 6 (a)²

SA = 6 in²

SA = 6 (161.29 × 2) in²

SA = 6 (322.58) in²