Question

5. Solve the following word problems: (a) The table given below shows a pattern of cubes formed using matchsticks. Write an expression for the number of matchsticks needed to make a pattern with n cubes Number of Cubes Diagram 1 2 3 n​

Answer 1

Answer:

Given :  a pattern of cubes using matchsticks

To Find  :   an expression for the number of matchsticks needed to make pattern with n cubes ​

Solution:

Matchsticks required for one cube = 12

Matchsticks required for two cubes = 12 + 8 = 20

Matchsticks required for 3 cubes = 12 + 8 + 8 = 20 + 8  = 28  

and so on...

1st cube required 12 match sticks  = 8 + 4

and then further on each additional cubes required  8 matchsticks.

Hence  Matchsticks required for n cubes

= 12 + 8(n - 1)

= 12 + 8n - 8

= 8n + 4

Matchsticks required for n cubes = 8n + 4

expression for the number of matchsticks needed to make pattern with n cubes  is 8n + 4  

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