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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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