12. What is the length of the edge of a cube whose volume is 729 cm"?1

1.	12. What is the length of the edge of a cube whose volume is 729 cm"?13. Three numbers are in the ratio 2:3:4. The sum of their cubes is 271656. Find thnumbers.
Answer» Answer: 12. The length of the EDGE of the cube is 9 cm. 13. The NUMBERS are 2x14 = 28, 3x14 = 42, and 4x14 = 56. Step-by-step explanation: 12. LET's assume that, the length of the edge of the cube is x. ∴ $x^3$ = 729 = 3.3.3.3.3.3 = $3^3.3^3$ $=9^3$ ∴ $x = 9 cm$ 13. Three numbers are in the ratio 2:3:4 If the first number is 2x, then the other two are 3X and 4x According to the problem: $(2x)^3 + (3x)^3 + (4x)^3$ = 271656 $=>8x^3 + 27x^3 + 64x^3$ = 2.2.2.3.3.11.7.7.7 $=>99x^3$ = 99.2.2.2.7.7.7 $=> x^3 = 2^3.7^3$ ∴ $x = 14$ ∴ The numbers are 2x14 = 28, 3x14 = 42, and 4x14 = 56.