Volumes Practice Test 1

Let the sides of the three cubes are 3x, 4x and 5x cm respectively,
${\left(3\mathit{x}\right)}^3+{\left(4\mathit{x}\right)}^3+{\left(5\mathit{x}\right)}^3$ = ${\left(\frac{12\sqrt{3}}{\sqrt{3}}\right)}^3$
⇒ $27{\mathit{x}}^3+64{\mathit{x}}^3+125{\mathit{x}}^3$ = 12 × 12 × 12
⇒ $216{\mathit{x}}^3$ = 12 × 12 × 12
⇒ ${\mathit{x}}^3$ = $\frac{12\times 12\times 12}{26}$ = 8
∴ x = 2
Hence, its sides are 6 cm, 8 cm and 10 cm respectively.