Question

the dimensions of a cuboid are in the ratio 1:2:3 and its total surface is 88cm². find its dimensions also find its volume.​

Answer 1

Answer :

• The dimensions of cuboid is 2cm × 4cm × 6 cm
• The volume of cuboid is 48 cm³

Step-by-step explanation :

To Find,

• The dimensions
• The volume

Solution,

Given that,

• The dimensions of a cuboid are in the ratio 1:2:3
• Total surface area = 88 cm²

Let us assume the lenght, breadth and height as 1x , 2x and 3x respectively.

As we know that,

Total surface area of cuboid = 2( lb + bh + hl )

Where,

• l = Length
• b = Breadth
• h = Height

Therefore,

» 88 = 2 ( x × 2x + 2x × 3x + x × 3x )

» 88 = 2 ( 2x² + 6x² + 3x² )

» 88 = 2 × 11x²

» 88 = 22x²

» x² = 88 / 22

» x² = 4

» x = √4

» x = 2

Hence, the value of x is 2. So,

Lenght ( we assumed lenght as x )

» 1 × x

» 1 × 2

» 2 cm

Breadth ( we assumed breadth as 2x )

» 2 × x

» 2 × 2

» 4 cm

Height ( we assumed height as 3x )

» 3 × x

» 3 × 2

» 6 cm

∴ The dimensions are 2 cm × 4 cm × 6 cm.

Now, the volume of cuboid is,

As we know that,

Volume of cuboid = ( Length × Breadth × Height )

Therefore, volume

» ( 2 × 4 × 6 )

» ( 8 × 6 )

» 48 cm³

∴ The volume of cuboid is 48 cm³.