Question

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 th
numbers.​

Answer 1

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.