Question

the Length breadth and height of a cuboid are in the ratio 3 :4 :6 and its volume is 576 cm cube . find the whole surface area of cuboid

Answer 1

let the length be 3x.
breadth be 4x
and the height be 6x.
so,
3x*4x*6x=576
${x}^{3} = \frac{576}{72} = 8$
$x = 2$
so the length, breadth ,height become (6,8,12) cm respectively.
the whole surface area = 2(lb+bh+hl)=2(48+96+72)=2(216)=532 cm²

Answer 2

Answer:

432 sq cm

Step-by-step explanation:

L:B:H = 3:4:6

Let L = 3x, B=4x, C=6x

Volume = 576 cu.cm

L×B×H = 576

3x × 4x × 6x = 576

72$x^{3}$ = 576

$x^{3}$ = 8 => x = 2

∴ L = 6cm , B =8cm and H = 12cm

Total surface area = 2×(LB+BH+HL)

                              = 2(6×8 + 12×8 + 12×6) = 2(48 + 96 + 72)

                             = 432 sq cm