Question

The length, breadth and height of a cuboid are in the ratio 6:5:3. If the total surface area is 504 cm², find its dimension. Also find the volume of the cuboid.

Answer 1

Heyy mate❤✌✌❤

here's your Answer ....

let the length, breadth and height of a cuboid be 6x , 5x and 3x respectively.

=> Total surface area = 2( lb + bh + hl)

=> 504 = 2( 6x × 5x + 5x × 3x + 3x × 6x)

=> 504 = 2( 30x^2 + 15x^2 + 18x^2)

=> 504 = 2× 63x^2

=> 504 = 126x^2

=> x^2 = 504 / 126

=> x^2 = 4

=> x = 2cm.

So, length = 12cm, Breadth = 10cm and Height =6cm

Volume of Cyboid = l × b × h.

=> v = 12 × 10 × 6

=> v = 12 × 60

=> volume = 720cm^3.
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Answer 2

Solution :

Let l , b, h are length , breadth and

height of a cuboid respectively ,

l : b : h = 6 : 5 : 3 [ given ]

Let l = 6x cm ,

b = 5x cm ,

h = 3x cm

i )Total Surface Area of the cuboid=504cm²

=> 2( lb + bh + lh ) = 504

=> 2[ 6x*5x + 5x*3x + 6x*3x ] = 504

=> 2( 30x² + 15x² + 18x² ) = 504

=> 2 × 63x² = 504

=> x² = 504 /( 2 × 63 )

After cancellation ,we get

=> x² = 4

=> x = 2

Therefore ,

l = 6x = 6 × 2 = 12 cm

b = 5x = 5 × 2 = 10 cm

h = 3x = 3 × 2 = 6 cm

ii ) Volume of the Cuboid ( V ) = lbh

=> V = 12 cm × 10 cm × 6cm

=> V = 720 cm³

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