Answer:

total surface area=2(lb+bh+ hl)=414cm²

Step-by-step explanation:

let the edges of the cuboid be x ,2x,7x ( as given ratios) -----------------------(1)

volume = l×b×h = 378. cm³

x(2x)(7x)= 378

14x³= 378

x³= 27

x=3

putting 3 in eq 1 we find edges of cuboid as 3,6,21

total surface area= 2(lb+bh+hl)

=2(3×6+6×21×3)

=2(18+126+63)

=2(207)

=414cm²

Answer:

414cm²

Step-by-step explanation:

For the cuboid,

Volume = 378 cm³

Let the edges be 1x, 2x and 3x

Therefore, Volume = lbh

=1x×2x×7x

= 14x³

By the condition

14x³ = 378

or, x³ = 378/14

or, x³ = 27

or, x = √√27

or, x= 3

therefore, edges are 3 cm, 2×3=6cm, 7×3=21 cm

Therefore, Area of the cuboid=

2(lb +bh +lh) sq. unit

=2(3×6+6×21+3×21) sq. cm

=2(18+126+63)sq. cm

=2×207 sq. cm

= 414 cm²

Answer. Area of the cuboid is 414 cm²