If the areas of the adjacent faces of a rectangular block are in the r

1.	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 isA. 30 cmB. 20 cmC. 15 cmD. 10 cm
Answer» 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

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 isA. 30 cmB. 20 cmC. 15 cmD. 10 cm

Answer»

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