Question

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

A. 30 cm

B. 20 cm

C. 15 cm

D. 10 cm

Answer 1

Correct option is C. 15 cm

Given, Ratio of areas of adjacent faces of cube = 2 : 3 : 4

Volume of block = 9000 cm³

= A₁ : A₂: A₃ = 2 : 3 : 4

= bh : lb : lh = 2 : 3 : 4

= b: l = 2 : 3

=h : l = 2 : 4

= h : b = 3 : 4 and v = lbh 

Assume that , l = 6x , b = 4x , h = 3x

= 6x \(\times\) 4x \(\times\) 3x = 9000

= x³ = \(\cfrac{9000}{72}\) = 125

= x = \(\sqrt[3]{125}\) = 5

So, smallest edge would be 3x = 3 × 5 = 15 cm