Question

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The dimensions of a cuboid are in ratio 1 : 2 : 3 and its total surface area is 88 m². Find the dimensions.​

Answer 1

★★Heya★★

Let the common ratio of dimensions in a cuboid be x.

Then dimensions of cuboid are

1x : 2x : 3x

ACCORDING TO THE QUESTION

2×{(1x × 2x ) + ( 2x × 3x ) + ( 1x × 3x)} = 88

2×(2x² + 6x² + 3x²) = 88

11x² = 44

x² = 4

x = 2

x = 2

So, the dimensions of cuboid are

2 , 2 × 2 And 3 × 2

2m , 4m And 6m

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Total Surface area of cuboid having dimensions L , B And H is

2 × ( LB + BH + HL )

Answer 2

$\huge{\mathfrak{Solution :-}}$

Since the dimensions of the cuboid are in ratio 1 : 2 : 3.

So, Let the Dimensions be x, 2x and 3x in metres.

Now,

   Surface Area = 88 cm²

⇒ 2(x × 2x + 2x × 3x + 3x × x) = 88

⇒ 2(2x² + 6x² + 3x²) = 88

⇒ 2 × 11x² = 88

⇒ 22x² = 88

⇒ x² = $\dfrac{88}{22}$

⇒ x² = 4

⇒ x = 2 m

∴  2x = 2 × 2 = 4 m and  3x = 3 × 2 = 6 m

Hence, the dimensions are 2 m, 4 m and 6 m.