Question

The length, breadth, and height fo a cuboid are in the ratio 3:4:6 and its volume is 576 cm3 (cm cube). The whole surface of the cuboid is ?

Answer 1

volume of cuboid=lbh
                    576=3x×4x×6x
                    576=72x3(x cube)
               576/72=x3(x cube)
                       8=x3(x cube)
                        2=x
sides are3x=6cm,4x=8,6x=12.
total surface area=2(lb+bh+hl)
                         =2(6×8+8×12+12×6)
                         =2(48+96+72)
                         =2×216
                         =432
total surface area of given cuboid is 432cm2(cm square).

Answer 2

Length breadth and height of the cuboid is given in the ratio 3:4:6
Let the length be 3x cm, breadth be 4x cm and height be 6x cm.
The volume of the cuboid is given as 576cm³
volume of any cuboid = lbh
∴3x* 4x* 6x = 576 cm³
⇒72x³ = 576 cm³
⇒x³ = 576 / 72 
⇒x³ = 8
⇒x = 2 cm
∴length = 3x = 6cm
breadth = 4x = 8cm
height = 6x = 12cm
Total surface area = 2( lb + bh + hl)
⇒2[(6*8) + (8*12) + (12*6)
⇒2(48 + 96 + 72)
⇒2(216)
⇒432 cm²