Question

How many multiples of 9 can be found which are less than 9999 and are perfect cubes?

Answer 1

Answer:

the answer is 7

starting from 3 cube to 21 cube

3 cube, 6 cube, 9 cube, 12 cube, 15 cube, 18 cube and 21 cube.

Step-by-step explanation:

Answer 2

Given:

The set of numbers between 1 and 9999.

To Find:

The numbers from the above set that are the multiples of 9 and are also perfect cubes are?

Solution:

1. The value of the perfect cube numbers from 1 to 9999 are,

=> 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261.

2. For a number to be divisible by 9, the sum of the digits of the number must be a multiple of 9.

=> Sum of the digits,

=> 27 = 2 + 7 = 9,

=> 216 = 2 + 1 + 6 = 9,

=> 729 = 7 + 2 + 9 = 18,

=> 1728 = 1 + 7 + 2 + 8 = 18,

=> 3375 = 3 + 3 + 7 + 5 = 18,

=> 5832 = 5 + 8 + 3 + 2 = 18,

=> 9261 = 9 + 2 + 6 + 1 = 18.

3. A total of 7 perfect cubes can be found which are less than 9999 and are multiples of 9.

Therefore, 9 multiples can be found.