SOLUTION: how many bricks,each of dimensions 20cm*12cm*9cm,will be required to build a wall 12m long 72cm thick 4m hight.

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Question 709234: how many bricks,each of dimensions 20cm*12cm*9cm,will be required to build a wall 12m long 72cm thick 4m hight.
Found 2 solutions by MathLover1, jsmallt9:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

bricks,each of dimensions 20cm%2A12cm%2A9cm, required to build a wall a=12m long, b=72cm thick h=4m+ height:
first find a volume of a wall: V%5Bw%5D=a%2Ab%2Ah
V%5Bw%5D=12m%2A72cm%2A4m.......b=72cm=%2872%2F100%29m=0.72m
V%5Bw%5D=12m%2A0.72m%2A4m
V%5Bw%5D=34.56m%5E3
now find a volume of a brick dimensions V%5Bb%5D=20cm%2A12cm%2A9cm
V%5Bb%5D=0.20m%2A0.12m%2A0.09m
V%5Bb%5D=0.00216m%5E3
now divide a volume of a wall by a volume of a brick
V%5Bw%5D%2FV%5Bb%5D=34.56m%5E3%2F0.00216m%5E3
V%5Bw%5D%2FV%5Bb%5D=34.56cross%28m%5E3%29%2F0.0021cross%286m%5E3%29
V%5Bw%5D%2FV%5Bb%5D=34.56%2F0.00216
V%5Bw%5D%2FV%5Bb%5D=16000....... bricks required to build a wall

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The solution from the other tutor is correct. But it is only correct because the each side of the wall can be divided evenly by a corresponding side of a brick. So a full, proper solution will first determine this divisibility.

The 20cm side of the brick will divide evenly into the 4m side of the wall: 4m = 400cm and 400/20 = 20

The 12cm side of the brick will divide evenly into the 12m side of the wall: 12m = 1200cm and 1200/12 = 100

The 9cm side of the brick will divide evenly into the 72cm side of the wall: 72/9 = 8

This makes the number of bricks needed: 20*100*8 = 16000 (which matches the answer from the other tutor).

P.S. When checking for the divisibility, try all possible combinations. In this problem, the 20cm side of the brick divides into both the 12m and 4m sides of the wall. The 12cm side of the brick divides into both the 72cm and 12m sides of the wall. But the 9cm side of the brick only divides evenly into the 72cm side of the wall. This leaves the 12m for the 12cm and then the 20cm into the 4m.

P.P.S. If you cannot find this divisibility then it will not be possible to build the wall unless you break off parts of the bricks. This is a more difficult problem to solve and the solution from the other tutor, to divide the volumes, will not work correctly.