Question

Dimensions of a cuboid are in the ratio of 3:2:1 and its total surface area is 3168. find the length of cuboid

Answer 1

Heya!

Let its dimensions be x.

Then,
length = 3x
breadth=2x
height= x

Now,

TSA of cuboid = 3168

=) 2 (lb+bh+hl) = 3168

=) 2 (3x*2x+2x*x+x*3x) = 3168

=) 2 (6x^2+2x^2+3x^2) = 3168

=) 2 (11x^2) = 3168

=) 22x^2 = 3168

=) x^2 = 3168/22

=) x = root 144

=) x = 12

Then,

Length = 3x = 3×12 = 36 cm

Hope it helps u.

Answer 2

let the length be- 3y
let the breadth be - 2y
let the height be- 1y
tsa(total surface area)=2(lb+bh+hl)
3168=2(3y*2y + 2y*1y + 1y*3y)
3168/2= 6y^2 + 2y^2 + 3y^2
1584= 11y^2
y^2= 1584/11= 144
y=root of 144
y= 12
length=3y=3*12= 36
breadth=2y=12*2= 24
height=y=12

hope it is clear...