Question

the length, breadth,height of a cuboid are in a the ratio 7:6:5. If the surface area of the cuboid is 1926 cm squared, find the volume of the cuboid.

Answer 1

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let l=7x b=6x h=5x   
S.A. of cuboid=2[lb+bh+hl]
1926=2[7x × 6x + 6x × 5x + 5x × 7x]
1926=2[42x^2+30x^2+35x^2]
1926=2X107x^2
107x^2=1926/2=963
x^2=963/107=9
x=3
V=21X18X15=5670cm^3
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Answer 2

Answer :

The volume of cuboid is 5670 cm³

Step-by-step explanation :

Let the length, breath and height of the cuboid be 7x, 6x and 5x respectively.

According to the question ;

Surface area of cuboid = 1926 cm²

⇒ 2 ( lb + bh + hl ) = 1926

⇒ 2 ( 7x * 6x + 6x * 5x + 5x * 7x ) = 1926

⇒  ( 42 x² + 30 x² + 35x² ) = 1926 / 2

⇒ 107 x² = 963

⇒ x² = 963 / 107

⇒ x² = 9

⇒ x = √9

⇒ x = 3

Therefore, the length, breath and height of the cuboid are ;

Length (l) = 7 * 3 = 21 cm.

Breadth (b) = 6 * 3 = 18 cm.

Height (h) = 5 * 3 = 15 cm.

Volume of cuboid = l × b × h

                              = 21 × 18 × 15

                              = 5670 cm³