Page 64 - Mathematics Class - XI

4. Fix 1 , i.e., 1, thermocol ball with the help of a pin at the square on the upper left most corner
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as shown in Fig. (b). Note the square as enclosure I.

5. Fix 2 , i.e., 8, thermocol balls with the help of 8 pins on the same square sheet in 8 squares adjacent to
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the previous square as shown in Fig. (b). Note the square formed by total (1 + 8) thermocol balls as
enclosure II.

6. Fix 3 , i.e., 27, thermocol balls with the help of 27 pins on the same square sheet in 27 squares adjacent to
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the previous 8 squares as shown in Fig. (b). Note the square formed by total (1 + 8 + 27) thermocol balls
as enclosure III.

7. Fix 4 , i.e., 64, thermocol balls with the help of 64 pins on the same square sheet in 64 squares adjacent to
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the previous 27 squares as shown in Fig. (b). Note the square formed by total (1 + 8 + 27 + 64) thermocol
balls as enclosure IV.

8. Fix 5 , i.e., 125, thermocol balls with the help of 125 pins on the same square sheet in 125 squares adjacent
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to the previous 64 squares as shown in Fig. (b). Note the square formed by total (1 + 8 + 27 + 64 + 125)
thermocol balls as enclosure V.

Fig. (b)

DEMONSTRATION

1. Number of thermocol balls in enclosure I = 1 = 1
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2. Total number of thermocol balls in enclosure II = 1 + 2 = 1 + 8 = 9
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