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Question
The circumference of a circle is equal to the side of a square whose area measures 407044 sq. cms. What is the area of the circle ?
Is it possible to solve this question using digital root method?
The circumference of a circle is equal to the side of a square whose area measures 407044 sq. cms. What is the area of the circle ?
Is it possible to solve this question using digital root method?
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Solution
The correct option is E Cannot be determined
Area of square = 407044 sq.cm
Side of square = sqrt 407044 = 638 cm
So, circumference of the circle = 638 cm
2*Pi*R = 638
R = (638/(3.14 *2)) = 197.1 cm
Area of circle = Pi *R *R = 3.14 * 197.1 * 197.1 = 122004.9 sq.cm
Digital Root :
To obtain the digital root of number we simply add the digits, and continue to do so until we are left with a single digit . For example:
1 244 > 11 > 2 so the digital root of 1 244 is 2
24 675 > 24 > 6 so the digital root of 4 675 is 6
We often discover that, when you have to obtain the digital root of a large number , you only need to count one out of all the 9's it contains. For example:
If we take the number 4 569 512 597 853, losing one of the two 9's gives you 456 951 257 853.
Then you can do the same with numbers that add to 9 [ as we know that when added to the 9 we have kept , the resulting sum will be multiple of 9 and will therefore have a digital root of 9 ]. So in the number we have now, we can also lose 4 & 5, 6 & 3, 1 & 8, 2 & 7 which leaves 9 555.
Now we can find the digital root of 9 555 quite easily : 9+5+5+5=24, then 2+4=6
That's nice - no big additions to do to get the digital root of 4 569 512 597 853 to be 6.
It is generally used for the fast arithmetical calculations. So , it is not applicable to the given problem directly.
Area of square = 407044 sq.cm
Side of square = sqrt 407044 = 638 cm
So, circumference of the circle = 638 cm
2*Pi*R = 638
R = (638/(3.14 *2)) = 197.1 cm
Area of circle = Pi *R *R = 3.14 * 197.1 * 197.1 = 122004.9 sq.cm
Digital Root :
To obtain the digital root of number we simply add the digits, and continue to do so until we are left with a single digit . For example:
1 244 > 11 > 2 so the digital root of 1 244 is 2
24 675 > 24 > 6 so the digital root of 4 675 is 6
We often discover that, when you have to obtain the digital root of a large number , you only need to count one out of all the 9's it contains. For example:
If we take the number 4 569 512 597 853, losing one of the two 9's gives you 456 951 257 853.
Then you can do the same with numbers that add to 9 [ as we know that when added to the 9 we have kept , the resulting sum will be multiple of 9 and will therefore have a digital root of 9 ]. So in the number we have now, we can also lose 4 & 5, 6 & 3, 1 & 8, 2 & 7 which leaves 9 555.
Now we can find the digital root of 9 555 quite easily : 9+5+5+5=24, then 2+4=6
That's nice - no big additions to do to get the digital root of 4 569 512 597 853 to be 6.
It is generally used for the fast arithmetical calculations. So , it is not applicable to the given problem directly.
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