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
[tex] \sqrt{2a ^{2} } [/tex] = [tex] \sqrt{(25.4) ^{2} } [/tex]
a = [tex]( \frac{25.4 in}{ \sqrt{2} })( \frac{ \sqrt{2} }{ \sqrt{2} } ) [/tex]
a = [tex] \frac{25.4in \sqrt{2} }{2} [/tex]
a = [tex]12.7 \sqrt{2} [/tex] in
VOLUME OF INSCRIBED CUBE:
Volume = a³
Volume = (12.7 [tex] \sqrt{2} [/tex])³
Volume = 2,048.38 (2) [tex] \sqrt{2} [/tex] in³
Volume ≈ 4,096.76 (1.4142) in³
Volume ≈ 5,793.64 in³
SURFACE AREA OF CUBE:
SA = 6 (a)²
SA = 6 [tex](12.7 \sqrt{2} ) ^{2} [/tex] in²
SA = 6 (161.29 × 2) in²
SA = 6 (322.58) in²
Surface Area ≈ 1,935.48 in²