Question

The edges of a cuboid are in ratio 1:2:3 and its volume is 1296 cu. cm. Find its length, breadth and height.​

Answer 1

Answer:

Step-by-step explanation:

Let the common ratio be x

let length = x

breadth =2x

height = 3x

volume of  cuboid is lenght*breadth*height

1296=x*2x*3x

6x^3=1296

x=6

lenght=6

breadth=12

height=18

Answer 2

Given,

• The edges of the cuboid are in the ratio of 1:2:3
• The volume of the cuboid = 1296 cm³

To find,

• Length, breadth, and height of the cuboid

Solution,

The length, breadth, and height of the cuboid are 6 cm, 12 cm, and 18 cm.

Let the constant of ratio be 'x'

Length of the cuboid = x

The breadth of the cuboid = 2x

Height of the cuboid = 3x

Volume of the cuboid = length * breadth * height

                                      = x * 2x * 3x

                                     = 6x³

But the volume of the cuboid = 1296 cm³

then,                      6x³  = 1296

                                x³  = 1296/6

                                x³  = 216

                                  x  = 6

∴ The length of the cuboid = 6 cm

          breadth of the cuboid = 12 cm

           height of the cuboid = 18 cm

Hence, The length, breadth, and height of the cuboid are 6 cm, 12 cm, and 18 cm.