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problems on surface area of cubes

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Problems on volume and surface area of cubes
Number
10
20
30
40
50
60
70
80
90
100
Cube
1000
8000
27000
640000
125000
216000
343000
512000
729000
100000

By observing the above table
1.       If the cube is below 1000 then the cuberoot  is below 10
2.       If the cube is between 1000 to 8000, then the cuberooe is between 11 to 20.
3.       If the cube is between 8001 to 27000, then the cuberoot is between 21 to 30
4.       If the cube is between 27001 to 64000, then the cuberoot  is between 31 to 40
5.       If the cube is between 64001 to 125000, then the cuberoot  is between 41 to 50.
6.       If the cube is between 125001 to 216000, then the cuberoot  is between 51 to 60.
7.       If the cube is between 216000 to 343001, then the cuberoot is between 61 to 70.
8.       If the cube is between 343001 to 512000, then the cuberoot  is between 71 to 80.
9.       If the cube is between 512001 to 729000, then the cuberoot  is between 81 to 90.
        If the cube is between 729001 to 100000, then the cuberoot  is between 91 to 100.

Number(last digit in number)
Last digit in cube
Easy identification for number(last digit in number)

1
1
1

2
8
2(10-8)

3
7
3(10-7)

4
4
4

5
5
5

6
6
6

7
3
7(10-3)

8
2
8(10-2)

9
9
9

10
0
0


By seeing the above table when the last digit in the cube is 1,4,5,6,9,0 the the last digit in the cube root also same. But when the last digit in the cube is 2,3,8,7 then subtract these digits from 10, then the last digit in cuberoot number will appear.
Now we will see for the cube related problems.
Volume of a cube surface=sidexsidexside=side 3
Surface area of a cube=6xside2
Problem1:volume of a cube is 1728 cm 3 . what is the side of a cube?
Step1:volume of a cube =1728= side 3
Step2:find the cubic root of 1728
Step3:last digit in cube is 8. Last digit in cube root is 2
Step4:cube is between 1000 to 8000. So cuberoot exist between 10 to 20.
Step4:so cuberoot is 12. That is side of a cube is 12cm.

Problem2:volume of a cube is 729 cm 3 . what is the side of a cube?
Step1:volume of a cube =729= side 3
Step2:find the cubic root of 729
Step3:last digit in cube is 9. Last digit in cube root is 9
Step4:cube is below 1000 . So cuberoot exist below 10.
Step4:so cuberoot is 9. That is side of a cube is 9cm.

Problem3:volume of a cube is 1331 cm 3 . what is the surface area of a cube?
Step1:volume of a cube =1331= side 3
Step2:find the cubic root of 1331
Step3:last digit in cube is 1. Last digit in cube root is 1
Step4:cube is between 1000 to 8000. So cuberoot exist between 10 to 20.
Step4:so cuberoot is 11. That is side of a cube is 11.
Step5: surface area of a cube is  =6xside2 =6x11x11=726cm2


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