Question

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Length breadth and height of a cuboid are in the ratio 7:6:5 with the surface area of a cuboid is 1926cm2 find its volume??? urgentplease answer

Answer 1

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

Hence, the volume of cuboid is 5670 cm³.

Answer 2

$\mathbb{ELLO \ THERE!}$

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Question: The length, breadth and the height of a cuboid are in the ratio 7:6:5 and the surface area of a cuboid is 1926cm². Find the volume.

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$\underline{\large\boxed{\mathsf{ANSWER}}}$

5760cm³

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Step-by-Step Explanation ↓

Given values

$\ell$ = 7x

b = 6x

h = 5x

Surface area of cuboid = 1926cm²

To find

Volume of cuboid.

Solution

Surface area of the cuboid = 1926cm²

2[$\ell$b + bh + $\ell$h] = 1926

2[{7x × 6x} + {6x × 5x} + {7x × 5x}] = 1926

2[42x² + 30x² + 35x²}] = 1926

2[107x²] = 1962

107x² = $\mathsf{\frac{1962}{2}}$

107x² = 963

x² = $\mathsf{\frac{963}{107}}$

x² = 9

x = $\mathsf{\sqrt{9}}$

x = 3

Substituting 'x' in lenght, breadth and height.

$\ell$ = 7[3] = 21

b = 6[3] = 18

h = 5[3] = 15

Finding Volume of the Cuboid

Vol. of a cuboid = $\ell$ × b × h

                           = 21 × 18 × 15

                           = 21 × 270  

                           = 5670cm³

Therefore the volume of the cuboid is 5760cm³

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Hope it Helps!

@Tomboyish44