### Solution:

Given,Decorative block is made up of a cube and a hemisphere.

The diameter of the hemisphere = 4.2cm

The edge of the cube = 6cm

The formula for the total surface area of a cube is $\n \n 6\n a\n 2\n \n \n $ where a is the edge of the cube. The formula for the curved surface area of a hemisphere of radius, r is given by $\n \n 2\pi \n r\n 2\n \n \n $ . The radius is half of the diameter.

We have to find the total surface area of the block.

As, the diameter of the hemisphere = 4.2cm, so the radius of the hemisphere is $\n \n \n \n r=\n \n 4.2\n 2\n \n \n \n \n \n \n \u21d2r=2.1cm\n \n \n \n \n $

The curved surface area of the hemisphere is given by $\n \n CSA=2\pi \n r\n 2\n \n \n $ .

We get,

$\n \n \n \n CSA=2\pi \n (2.1)\n 2\n \n \n \n \n \n \n \u21d2CSA=2\xd7\n \n 22\n 7\n \n \xd72.1\xd72.1\n \n \n \n \n \u21d2CSA=27.72c\n m\n 2\n \n \n \n \n \n \n $

Now, the edge of a cube is 6cm.

The total surface are of a cube of edge a is given by $\n \n TS\n A\n c\n \n =6\n a\n 2\n \n \n $

We get,

$\n \n \n \n TS\n A\n c\n \n =6\n \n 6\n \n 2\n \n \n \n \n \n \n \u21d2TS\n A\n c\n \n =6\xd76\xd76\n \n \n \n \n \u21d2TS\n A\n c\n \n =216c\n m\n 2\n \n \n \n \n \n \n $

The total surface area of the block = total surface area of cube – base area of hemisphere + curved surface area of hemisphere

Base area of hemisphere is $\n \n \n A\n b\n \n =\pi \n r\n 2\n \n \n $

We get,

$\n \n \n \n \n A\n b\n \n =\n \n 22\n 7\n \n \xd7\n (2.1)\n 2\n \n \n \n \n \n \n \u21d2\n A\n b\n \n =\n \n 22\n 7\n \n \xd72.1\xd72.1\n \n \n \n \n \u21d2\n A\n b\n \n =13.86c\n m\n 2\n \n \n \n \n \n \n $

The total surface area of the block = $\n \n =TS\n A\n c\n \n \u2212\n A\n b\n \n +CSA\n $

We get,

$\n \n \n \n TSA=216\u221213.86+27.72\n \n \n \n \n \u21d2TSA=229.86c\n m\n 2\n \n \n \n \n \n \n $

Thus, the total surface area of the block is $\n \n 229.86c\n m\n 2\n \n \n $ .

Hence, the correct option is 2.