Question

the surface area of a cuboid is 1,372 sq cm if the dimension of the cuboid are in the ratio of 4:2:1 find its dimensions​

Answer 1

Step-by-step explanation:

Let the length be 4x  and breadth be 2x  and height be x

Surface area=2(lb + bh + hl)

1372 = 2(8x² + 2x² + 4x²)

1372 = 28x²

⇒ x²=49

⇒ x=7

So,

length = 28 cm

breadth = 14 cm

Height = 7 cm

Hope it helps!

Answer 2

Answer:

• Length = 28 cm

• Breadth = 14 cm

• Height = 7 cm

Step-by-step explanation:

Given:

• Total surface area of cuboid = 1372 cm²
• Dimension of cuboid are in ratio = 4:2:1

To Find:

• Dimension of cuboid.

Let dimension of cuboid are:

• Length (l) = 4x
• Breadth (b) = 2x
• Height (h) = x

Now, by using Total surface area formula we will calculate its dimensions,

⇒ Total surface area of cuboid = 2(lb + bh + hl)

⇒ 1372 = 2(4x × 2x + 2x × x + x × 4x)

⇒ 1372 = 2(8x² + 2x² + 4x²)

⇒ 1372 = 2(14x²)

⇒ 1372 = 28x²

⇒ x² = 1372/28

⇒ x² = 49

⇒ x = √49

⇒ x = 7 cm

Hence, dimensions are:

• Length = 4x = 4 × 7 = 28 cm
• Breadth = 2x = 2 × 7 = 14 cm
• Height = x = 7 cm

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