Question

The Length, breadth and height of a cuboid are in the ratio 6 : 5 : 3 .If its total surface area is 504 cm2 , Also find the volume of the cuboid.
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Answer 1

Answer:

Let the length of Cuboid be 6x

breadth of cuboid be 5x

height of cuboid be 3x

Area of cuboid = 504 sq. cm

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

=> 6x×5x + 5x×3x + 6x×3x = 504/2

=> 30x^2 + 15x^2 + 18x^2 = 252

=> 63x^2 = 252

=> x^2 = 252/63

=> x^2 = 4

=> x = √4

=> x = 2

Length = 6x = 6×2 = 12cm

Breadth = 5x = 5×2 = 10cm

Height = 3x = 3×2 = 6cm

Now ,

Vol. = L × B × H

= 12 × 10 × 6

= 720 cm^3

Hence , The volume of the cuboid is 720 cm^3 .

Hope it helps you...

Answer 2

Step-by-step explanation:

let,

the length is 6k

the breadth is 5k

the height is 3k

(here k is non zero constant )

Total surface area = 2(lb +bh+lh)

$2(6k \times 5 k+ 5 k\times 3k + 6 k\times 3k) \\ 2(30 {k}^{2} + 15 {k}^{2} + 18 {k}^{2} ) \\ 2(63 {k}^{2} ) = 126 {k}^{2}$

According to question

$126 {k}^{2} = 504 \\ 63 {k}^{2} = 252 \\ 9 {k}^{2} = 36 \\ {k}^{2} = 4 \\ k = 2$

so,

length is 6×2= 12 cm

breadth is 5×2= 10 cm

height is 3×2= 6cm

therefore volume = 12 ×10×6 = 720 cm³