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If the areas of the adjacent faces of a rectangular block are in the ratio 2 : 3 : 4 and its volume is 9000 cm3, then the length of the shortest edge is - Mathematics

MCQ

If the areas of the adjacent faces of a rectangular block are in the ratio 2 : 3 : 4 and its volume is 9000 cm3, then the length of the shortest edge is

Options

  •  30 cm

  • 20 cm

  •  15 cm

  •  10 cm

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Solution

Let, the edges of the cuboid be a cm, b cm and c cm.

And, a < b < c

The areas of the three adjacent faces are in the ratio 2 : 3 : 4.

So,

ab : ca : bc = 2 : 3 : 4, and its volume is 9000 cm3

We have to find the shortest edge of the cuboid

Since;

`(ab)/(bc) = 2/4`

`a/c = 1/2`

   c = 2a

Similarly,

`(ca)/(bc) = 3/4`

`a/b = 3/4`

`b = (4a)/3`

`b = (4a)/3`

Volume of the cuboid,

   V = abc 

`9000 = a((4a)/3)(2a)`

27000 = 8a3

      a=` (27 xx1000)/8`

     `a = (3xx10)/2`

       a = 15 cm 

As` b = (4a)/3 `and c = 2a 

Thus, length of the shortest edge is 15 cm .

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 18 Surface Areas and Volume of a Cuboid and Cube
Q 7.2 | Page 35
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