Question

the length ,breadh and height of a cuboid are in the ratio7:6:5 If the surface area of the cuboid is 1926cm2findthe volume of the cuboid​

Answer 1

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Answer:

Step-by-step explanation:

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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

hope this helps.

Answer 2

Given :-

The length, breadth and height of a cuboid is 7:6:5

The Total Surface Area of the cuboid is 1926 cm²

To be found :

The volume of the cuboid.

Let,

length be 7x cm

breadth be 6x cm

height be 5x cm

We know that,

Total Surface Area of cuboid = 2(lb+bh+hl) unit sq.

[ ∴ In which l is the length, b is the breadth and h is the height ]

⇒ 1926 = 2(lb + bh + hl)

⇒ 1926 = 2(7x*6x + 6x*5x + 5x*7x)

⇒ 1926 = 2(42x² + 30x² + 35x²)

⇒ 1926 = 2(107x²)

⇒ 1926 = 214x²

⇒ 1926 ÷ 214 = x²

⇒ 9 = x²

⇒ √9 = x

⇒ 3 = x

∴ value of x = 3

So,

length of the cuboid = 7x = 7*3 = 21 cm

breadth of the cuboid = 6x = 6*3 = 18 cm

height of the cuboid = 5x = 5*3 = 15 cm

Now,

Volume of the cuboid

Formula = lbh  unit cube

[∴ In which l is the length, b is the breadth, and h is the height ]

= 21*18*15

= 5670 cm³

Hence

the volume of the cuboid is 5670 cm³