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What is the total surface area of the cuboid? Statement I: The volume of the cuboid is 5184 cm3 and the ratio of the length, breadth and height of the cuboid is 3 : 4 : 2. Statement II: Total surface area of the upper and lower faces of the cuboid is 864 cm2 and the height of the cuboid is 12 cm.

What is the total surface area of the cuboid? Statement I: The volume of the cuboid is 5184 cm3 and the ratio of the length, breadth and height of the cuboid is 3 : 4 : 2. Statement II: Total surface area of the upper and lower faces of the cuboid is 864 cm2 and the height of the cuboid is 12 cm. Correct Answer Statement I alone is sufficient to answer the question.

Statement I:
Volume of the cuboid = lbh

Let length be 3x, breadth be 4x, height be 2x

5184 = 3x × 4x × 2x

⇒ 5184 = 24x3

⇒ 216 = x3

⇒ x = 6

Length = 18 cm, Breadth = 24 cm, Height = 12 cm

Total Surface Area of cuboid = 2 (lb + bh + hl)

⇒ 2 × (18 × 24 + 24 × 12 + 12 × 18)

⇒ 2 × (432 + 288 + 216)

⇒ 1872 cm2

Statement II:

Total surface area of the upper and lower faces of the cuboid is 864 cm2

2lb = 864

⇒ lb = 432

height (h) = 12 cm

Now,

Total Surface Area of cuboid = 2 (lb + bh + hl)

We can’t find the total surface area as we do not have the values of length and breadth.

∴ Statement I alone is sufficient to answer the question.

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