Question

4. The length, breadth and height of a cuboid are
in the ratio 6:5: 3. If its total surface area is
504 cm?, find its dimensions. Also, find the
volume of the cuboid.​

Answer 1

Given :

⬤ Length , Breadth and Height of Cuboid are in the Ratio 6:5:3 .

⬤ Total Surface Area of Cuboid is 504 cm².

To Find :

⬤ Dimensions of Cuboid .

⬤ Volume of Cuboid .

Formula Used :

$\bf[\:{Total\:Surface\:Area\:of\:Cuboid=2(lb+bh+hl)}\:]$

Solution :

Let :

• Length of Cuboid be 6x.
• Breadth of Cuboid be 5x.
• Height of Cuboid be 3x.

According to the Formula :-

504 = 2(lb + bh + hl)

504 = 2(6x × 5x + 5x × 3x + 3x × 6x)

504 = 2(30x² + 15x² + 18x²)

504 = 2(63x²)

504 = 126x²

504/126 = x²

4 = x²

√4 = x

2 = x

Therefore , Value of x is 2 .

Hence ,

Length of Cuboid = 6x

= 6(2)

= 12

Breadth of Cuboid = 5x

= 5(2)

= 10

Height of Cuboid = 3x

= 3(2)

= 6

Therefore , Length , Breadth and Height of Cuboid is 12 cm , 10 cm and 6 cm .

Formula Used :

$\bf[\:{Volume\:of\:Cuboid=l\times{b}\times{h}\:]}$

Now :

According to the Formula :-

L × b × h

12 × 10 × 6

720 cm³

Therefore , Volume of Cuboid is 720 cm³ .