Answers

  • Brainly User
2016-01-05T15:03:27+08:00
Let a be the edge of the cube.  

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)
Diagonal = 2 (12.7 in)
               = 25.4 inches

Solve for edge (a) of cube, using Pythagorean Theorem:
diagonal = hyptonuse = 25.4 inches

(25.4 in)² = a² + a²

2a² = (25.4 in)²

 \sqrt{2a ^{2} }  \sqrt{(25.4) ^{2} }

a = ( \frac{25.4 in}{ \sqrt{2} })( \frac{ \sqrt{2} }{ \sqrt{2} } )

a =  \frac{25.4in \sqrt{2} }{2}

a = 12.7 \sqrt{2}  in

VOLUME OF INSCRIBED CUBE: 
Volume = a³
Volume = (12.7  \sqrt{2}
Volume = 2,048.38 (2)   \sqrt{2} in³
Volume ≈ 4,096.76 (1.4142) in³
Volume ≈ 5,793.64 in³

SURFACE AREA OF CUBE:
SA = 6 (a)²
SA = 6 (12.7 \sqrt{2} ) ^{2} in²
SA = 6 (161.29 × 2) in²
SA = 6 (322.58) in²
Surface Area  1,935.48 in²



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