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Question

The volume of a rectangular block of stone is 10368 m3. If its length, breadth and height are in the ratio 3 : 2 : 1, then its length, breadth and height are
  1. 12 m, 8 m, 4 m
  2. 36 m, 24 m, 12m
  3. 39 m, 26 m, 13 m
  4. 9 m, 6 m, 3 m


Solution

The correct option is B 36 m, 24 m, 12m

Given, length : breadth : height = 3 : 2 : 1
Let the height of block =x m
Then, length of block =3x m
          breadth of block =2x m    

Volume of the block of stone
=3x×2x×x=6x3 m3
But it is given that volume of the stone = 10368 m3
   x3=103686=1728
 x=31728              =(12×12×12)13              =(123)13              =12 m

Hence, the length of the stone = 3 × 12 = 36 m
Breadth of the stone = 2 × 12 = 24 m
Height of the stone = 1 ×12 = 12 m

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