Question

If three equal cubes are placed adjacently in a row, then the ratio of the total surface area of the new cuboid to that of the sum of the surface areas of the three cubes will be

• A. 5 : 9
• B. 1: 3
• C. 2 : 3
• D. 7 : 9

Answer 1

The Correct Option is D

Let's take the sides of the cube be a.
Surface area = 6a²
The Surface area of 3 cubes will be = 6a² × 3 = 18a²
New cuboid formed will have:
length (l) = 3a
breadth(b) = a
height(h) = a
Surface area = 2[lb+bh+hl] = 2[3a×a + a×a + a×3a] = 14a²
Ratio of Surface Area = \(\frac{14 a^2}{18 a^2}\)
Surface Area Ratio = 7:9
The correct option is (D)