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Question

The volume of a rectangular block of stone is 10368 dm3. If its length, breadth, and height are in the ratio 3 : 2 : 1, then its length, breadth, and height are



A

36 dm, 18 dm, 4 dm

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B

36 dm, 24 dm, 12 dm

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C

18 dm, 14 dm, 36 dm

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D

36 dm, 18 m, 21 dm

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Solution

The correct option is C

36 dm, 24 dm, 12 dm


Let the length of block = 3x dm
Breadth of block = 2x dm    
Height of block = x dm
Volume of the block of stone
3x×2x×x=6x3 dm3
But the given volume of the stone = 10368 dm3
   x3=103686=1728
 x=31728=(12×12×12)13=(123)13=12
Hence, the length of the stone = 3 × 12 = 36 dm
Breadth of the stone = 2 × 12 = 24 dm
Height of the stone = 1 ×12 = 12 dm


Mathematics

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