Question

the dimension of a cuboid are in ratio 3:2:4 and its total surface area is 1404, find its dimension?

Answer 1

Answer:

Length 117 units, width 78 units , height 156 units

Step-by-step explanation:

formula of circumference of cuboid

=> 4( L+W+H) = 1404

=> 4( 3L/9 + 2w/9 + 4h/9) = 1404

=> 4/9( 3L+2w+4h) = 1404

=> 3L+2b+4h = 3159

=> Now divide 3159 in the ratio of dimension

length = 3159*3/9 = 117 units

width = 3159*2/9 = 78 units

height = 3159*4/9 = 156 units

Answer 2

Given:

1. Dimensions of cuboid in the ratio 3:2:4

2. Surface area : 1404 unit squared

To find : Dimensions of cuboid

Solution :

Let the sides of cuboid be 3x, 2x and 4x respectively.

Let the base has sides 3x and 2x.

Therefore, perimeter of base=

$2 \times (3x + 2x)$

$2 \times 5x$

$10x$

Surface area of sides =

$10x \: \times 4x$

$40 {x}^{2}$

Surface area of bases(there are two bases)=

$2 \times (3x \times 2x)$

$12 {x}^{2}$

Total surface area=

$52 {x}^{2}$

Therefore,

$52 {x}^{2} = 1404$

${x}^{2} = 27$

$x = \sqrt{27}$

$x = 5.196$

Sides of cuboid are :

$3x \: = 15.59$

$2x = 10.39$

$4x = 20.78$

Sides are 15.59, 10.39 and 20.78 units.