Question

Volume of a cube is 2744 cc. If two of its dimensions are doubled and the rest reduced by 300% then find out the ratio of the surface area between the original cube and the resultant figure.
1. 6 : 5
2. 4 : 5
3. 7 : 5
4. 3 : 4
5. cannot be determined

Answer 1

Correct Answer - Option 1 : 6 : 5

Given:

Volume of the cube = 2744 cc

Formula used:

Volume of cube = \({a^3}\) and surface area = \(6{a^2}\)

Where, a = length of each side of the cube

Surface area of cuboid = 2(lb + bh + lh) sq.cm.

Where, l, b & h are the length, breadth and height of the cuboid respectively.

Calculations:

Volume of the cube = 2744 cc

∴ Length of each side = \(\sqrt[3]{{2744}}\) = 14 cm

And, surface area = 6 × 14² = 1176 sq.cm.

After the changes, dimensions are = (2 × 14), (2 × 14) and (1/4 × 14) ⇒ 28, 28, 7/2 cm respectively. [Since, one dimension is reduced by 300%, it will become 1/4 times of before]

∴ Surface area = 2(28 × 7/2 + 28 × 7/2 + 28 × 28) sq.cm.

= 980 sq.cm.

Required ratio = 1176 : 980 = 6 : 5