Question

The dimensions of a cuboid are in the ratio 3:2:1 and its total surface area is 3168 cm2.Find its dimensions

Answer 1

Answers

Length(l) of the cuboid =  36cm.

Breath(b) of the cuboid = 24cm.

Height(h) of the cuboid = 12cm.

SOLUTION

Let us assume that the length(l) of the cuboid = 3x cm .

Let us assume that the breadth(b) of the cuboid = 2x cm.

Let us assume that the height(h) of the cuboid = x cm.

Total Surface area (TSA) of the cuboid = 3168 cm².

TSA of a cuboid = 2 (lb + bh + lh)

$\implies$ 2(3x×2x + 2x×x + 3x×x) = 3168

$\implies$ 2(6x² + 2x² + 3x²) = 3168

$\implies$ 2 × 11x² = 3168

$\implies$ 22x² = 3168

$\implies \sf x^2 = \dfrac{3168}{22}$

$\implies$ x² = 144

$\implies \sf x = \sqrt{144}$

$\implies$ x = 12

Length(l) of the cuboid = 3x = 3 × 12 = 36cm.

Breath(b) of the cuboid = 2x = 2 × 12 = 24cm.

Height(h) of the cuboid = x = 12cm.

Answer 2

Given :-

• The dimensions of a cuboid are in the ratio 3:2:1.
• Total surface area is 3168 cm².

To Find :-

• Measures of its Dimensions.

Solution :-

⟼ Let the Length be 3x

⟼ Let the Breadth be 2x

⟼ Let the Height be x

According to the Question :

➞ T.S.A of Cuboid = 2( lb + bh + hl )

➞ 3168 = 2( 3x * 2x + 2x * x + x * 3x )

➞ 3168 = 2( 6x² + 2x² + 3x² )

➞ 3168 / 2 = ( 6x² + 2x² + 3x² )

➞ 1584 = ( 6x² + 5x² )

➞ 1584 = 11x²

➞ 1584 / 11 = x²

➞ 144 = x²

➞ √144 = x

➞ 12 = x

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Therefore :

• Length = 3x = 3 × 12 = 36cm
• Breadth = 2x = 2 × 12 = 24cm
• Height = x = 12cm

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