Question

The dimensions of a cuboid are in the ratio 4:3:2 . If the total surface area of cuboid is 4212 sq. m; find the volume of cuboid.

Answer 1

T.S.A OF A CUBOID  =  2(lb+bh+lh)
​Let the values be x. So,
4x , 3x , 2x.
2(4x*3x+3x*2x+4x*2x)
2(12x​2 + 6x2 + 8x​2)
2*26x​2 = 4212
52x2 = 4212
x2 = 4212/52
x2 = 81
x = 9
4x = 36
3x = 27
2x = 18
Volume of a Cuboid = l*b*h
36*27*18 = 17496 m3

Answer 2

hello users ....

we have given that :
the length,breadth ,and height are in ratio of 4 : 3 :2 

and 

surface area of cuboid = 4212 m²

we have to find :
volume of cuboid =? 

solution :-
let the length of cuboid = 4x 
breadth of cuboid  = 3x 
and 
height of cuboid = 2x 

we know that :
Surface area of cuboid = 2 [ lb + bh + hl ] 

here,
2 [ lb + bh + hl ]  = 4212 m²

=> 2 [ 4x*3x + 3x*2x + 2x*4x] = 4212 m²

=> 2[ 12x² + 6x² + 8x²] = 4212 m²

=> 26 x² = 2106m²

=> x² = 2106 / 26 = 81 

=> x = 9 m

now 
length of cuboid = 4*9 = 36 m 
breadth of cuboid = 3*9 = 27 m
height of cuboid = 2*9 = 18 m

now,
we know that :
volume of cuboid = lbh 

= 36 * 27 * 18 = 17496 m³ answer 

✪✪ hope it helps ✪✪