# Find the Length, Breath, and Height of a Cuboid

The length , breath and height of a cuboid are in the ratio 3 : 4 : 6 and its volume is 576 cm^{3} . The whole surface of the cuboid is

- 216 cm
^{2} - 324 cm
^{2} - 432 cm
^{2} - 460 cm
^{2}

**Answer: (3) 432 cm ^{2}**

**Explanation:-**

Let be the length , breadth and height of the cuboid is 3X, 4X and 6X.

**Formula –**

**Volume of cuboid = lbh**

**where, l = length, b = breadth and h = height**

Then, 3X x 4X x 6X = 576

72X

^{3}= 576

X

^{3}= 576 / 72

X

^{3}= 8

Cube root of both side,

X = 2

Then, Length = 3X = 3 x 2 = 6cm, breadth = 4X = 4 x 2 = 8 cm and height = 6X = 6 x 2 = 12cm

Formula-

Whole surface area = 2(lb + bh + hl)

= 2 (6 x 8 + 8 x 12 + 12 x 6)

= 2(48 + 96 + 72)

= 2 x 216

= 432 cm square.

Hence, the answer is (3) 432 cm

^{2}