Question

What is the ratio of the volume of a cuboid to the volume of a cube?

Statement I. The ratio of the height, breadth, and length of the cuboid is 1 : 2 : 3 and the total surface area of the cuboid is 352 cm2.

Statement II. The total surface area of the cube is given to be 384 cm2.

Statement III. The length of the cuboid is 3 times the height of the cuboid and 1.5 times the breadth of the cuboid. The difference between the length and the height of the cuboid is 8 cm.

1.

The data in statement I alone is sufficient to answer the question, while the data in statement II and III alone are not sufficient to answer the question.

2. The data in statement II alone is sufficient to answer the question, while the data in statement I and III alone are not sufficient to answer the question.
3. The data in statement I and II or in statement II and III is sufficient to answer the question.
4. The data in all the statements I, II, and III are not sufficient to answer the question.
5. The data in all statements I, II, and III together are necessary to answer the question.

Answer 1

Correct Answer - Option 3 : The data in statement I and II or in statement II and III is sufficient to answer the question.

Calculation:

For Statement I:

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

Let Length be 3x, breadth = 2x, height = x

⇒ 352 = 2 (3x × 2x + 2x × x + x × 3x)

⇒ 176 = (6x² + 2x² + 3x²)

⇒ 176 = 11x²

⇒ x² = 16

⇒ x = 4

∴ Length = 12, Breadth = 8, Height = 4

∴ Volume = lbh

⇒ 12 × 8 × 4

⇒ 384 cm³

Statement I alone is not sufficient to answer the question.

For statement II:

Total Surface Area of Cube = 6s²

⇒ 384 = 6s²

⇒ s² = 64

⇒ s = 8

∴ Volume of the cube = s³

⇒ 8³

⇒ 512cm³

Statement II alone is not sufficient to answer the question.

For Statement III:

Height of the cuboid = x cm

Length = 3x

Breadth = 2x

∴ Difference = 3x – x

⇒ 8 = 2x

⇒ x = 4

∴ Length = 12, Breadth = 8, Height = 4

∴ Volume = lbh

⇒ 12 × 8 × 4

⇒ 384 cm³

Statement III alone is not sufficient to answer the question.

But we can solve the question by either Statement I and II or statement II and III.