What will be the cost of painting of the new shape? Eight small cubes each with an edge of 2cm are glued together to form a bigger cube as shown.

 Another small cube with an edge of 2cm is glued at the centre on top of the bigger cube. 

If the cost of painting is Rs 6/sq.cm, then what would be the cost of painting this new shape?


Here is what I have tried so far.....
Eight cubes of edge 2 cm are glued together.

So, the length of cuboid would become = 8 × 2 = 16 cm

Height and breadth would be the same i.e., 2 cm each

We know that, total surface area of the cuboid = 2(lb + bh + lh)
=2(16*2 +2*2+16*2) = 136 cm2

Surface Area of the smaller cube = 6*side2 = 6*22=6*4=24 cm2

Total area = 136+24 sq. cm = 160 sq.cm

Cost of painting at Rs 6/sq.cm = 160*6 =Rs 960/-

But the answer is Rs 672/-
Please help to understand where I'm wrong?
Thanks for the support
 A: To answer your question, we have to find the total exposed surface area of the entire shape. In your approach, you found the surface area of the larger cube (though incorrect) and added that to the surface area of the smaller cube. However, it is important to note that the smaller cube covers a small part of the top surface of the larger cube, and the base of the smaller cube is also covered by the larger cube.
First, let us find the surface area of the base and sides of the larger cube i.e. all the faces of the larger cube except for the top face.
The area of one face of the larger cube is as follows:

 $$(2 \text { cm} + 2 \text { cm}) \cdot (2 \text { cm} + 2 \text { cm}) = 4 \text { cm} \cdot 4 \text { cm} = 16 \text { cm}^2$$

Therefore, the area of the five faces of the larger cube (excluding the top face) is as follows:

 $$16 \text { cm}^2 \cdot 5 = 80 \text { cm}^2$$

To find the area of the top face of the larger cube that is exposed, we have to first have to find the area of one face of the smaller cube. The area of one face of the smaller cube is as follows:

 $$2 \text { cm} \cdot 2 \text { cm} = 4 \text { cm}^2$$

Therefore, to find the area of the top face of that larger cube that is exposed, we have to subtract the area of one face of the smaller cube from the area of one face of the larger cube. The area of the top face of the larger cube that is exposed is as follows:

 $$16 \text { cm}^2 - 4 \text { cm}^2 = 12 \text { cm}^2$$

The total surface area of the smaller cube that is exposed is the area of five faces (since the sixth is covered by the top of the larger cube). Therefore, the area of the five faces of the smaller cube is as follows:

 $$4 \text { cm}^2 \cdot 5 = 20 \text { cm}^2$$

Thus, the total exposed surface area of the entire shape is as follows:

 $$80 \text { cm}^2 + 12 \text { cm}^2 + 20 \text { cm}^2 = 112 \text { cm}^2$$

Since the cost of painting is Rs $6$/$\text {cm}^2$, the cost of painting the entire shape is as follows:

 $$112 \text { cm}^2 \cdot \text {Rs } 6/\text {cm}^2 = \text {Rs } 672$$

I hope that helps!
