Question

the surface area of a cuboid is 1372 sq cm. the dimensions of the cuboid are in ratio 4:2:1. find its dimensions​

Answer 1

$\sf{\huge{\underline{\blue{Given :-}}}}$

• The surface area of a cuboid is 1372 sq cm.

• The dimensions of the cuboid are in ratio 4:2:1

$\sf{\huge{\underline{\pink{To\:Find :-}}}}$

• The dimensions of a cuboid .

$\sf{\huge{\underline{\purple{Solution :-}}}}$

We have,

The dimensions of the cuboid are in ratio 4:2:1

Take in form of l = 4x, b = 2x & h = x .

Total Surface Area of Cuboid= 2(lb + bh +lh)

➝ 2 {(4x×2x)+(2x×x)+(x×4x) }

➝ 2 {(8x² +2x² + 4x²)}

➝ 2 × 14x²

➝ 28x²

We have, The surface area of a cuboid is 1372 sq cm.

➝ 28x² = 1372

➝ x² = $\cancel{\dfrac{1372}{28}}$

➝ x² = 49

➝ x = √49

➝ x = 7

• Length = 4x = 4 × 7 = 28

• Breadth = 2x = 2 × 7 = 14

• Hieght = x = 7

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Answer 2

Answer:

• The surface area of a cuboid is 1372 sq cm.
• The dimensions of the cuboid are in ratio 4:2:1

ToFind:−

The dimensions of a cuboid .

Solution:−

We have,

The dimensions of the cuboid are in ratio 4:2:1

Take in form of l = 4x, b = 2x & h = x .

Total Surface Area of Cuboid= 2(lb + bh +lh)

➝ 2 {(4x×2x)+(2x×x)+(x×4x) }

➝ 2 {(8x² +2x² + 4x²)}

➝ 2 × 14x²

➝ 28x²

We have, The surface area of a cuboid is 1372 sq cm.

➝ 28x² = 1372

➝ x² = \cancel{\dfrac{1372}{28}}

28

1372

➝ x² = 49

➝ x = √49

➝ x = 7

• Length = 4x = 4 × 7 = 28
• Breadth = 2x = 2 × 7 = 14
• Hieght = x = 7

________________________________