The ratio of the length of diagonal of two cubes is 2 ∶ 3 and the difference between the total surface area of the bigger cube and the lateral surface area of the smaller cube is 342 cm2. Find the total surface area of a statue which is formed by placing the smaller cube upon the bigger cube.?

Option 4 : 630 cm2

Calculation:

Since, diagonal ratio = side ratio of cube = 2 ∶ 3

Let the ratio be x

So, the side of the first cube = 2x

And the side of the second cube = 3x

According to question,

The total surface area of the bigger cube – Lateral surface area of smaller cube = 342

So, 6 (3x)² – 4 (2x)² = 342

⇒ 38x² = 342

So, x = 3

So, the side of the smaller cube = 2 × 3 = 6

And the side of the bigger cube = 3 × 3 = 9

So, the area of statue = total surface area of bigger cube + total surface area of the smaller cube – 2 × areas of one face of the smaller cube

So, the required area = 6 × 9² + 6 × 6² – 2 × 6²

Hence, 630 cm²