The Total Surface Area of the Block:

To find the total surface area of the decorative block, we need to calculate the surface area of both the cube and the hemisphere and then add them together.

Surface Area of the Cube:
The cube has a base with an edge length of 6 cm. Since all the sides of a cube are equal, the surface area of the cube is given by the formula:

Surface Area of the Cube = 6 × (Edge Length)^2

Substituting the given edge length of 6 cm into the formula, we can calculate the surface area of the cube:

Surface Area of the Cube = 6 × (6 cm)^2 = 6 × 36 cm^2 = 216 cm^2

Surface Area of the Hemisphere:
The hemisphere has a diameter of 4.2 cm, which means the radius is half of the diameter, or 2.1 cm. The surface area of the hemisphere can be found using the formula:

Surface Area of the Hemisphere = 2 × π × (Radius)^2

Substituting the given radius of 2.1 cm into the formula, we can calculate the surface area of the hemisphere:

Surface Area of the Hemisphere = 2 × π × (2.1 cm)^2 ≈ 2 × 3.14 × 4.41 cm^2 ≈ 27.78 cm^2

Total Surface Area of the Block:
To find the total surface area of the block, we add the surface area of the cube and the surface area of the hemisphere:

Total Surface Area of the Block = Surface Area of the Cube + Surface Area of the Hemisphere
= 216 cm^2 + 27.78 cm^2
≈ 243.78 cm^2

Therefore, the total surface area of the decorative block is approximately 243.78 cm^2.

The Volume of the Block:

To find the volume of the decorative block, we need to calculate the volume of both the cube and the hemisphere and then add them together.

Volume of the Cube:
The volume of a cube is given by the formula:

Volume of the Cube = (Edge Length)^3

Substituting the given edge length of 6 cm into the formula, we can calculate the volume of the cube:

Volume of the Cube = (6 cm)^3 = 6 × 6 × 6 cm^3 = 216 cm^3

Volume of the Hemisphere:
The volume of a hemisphere can be found using the formula:

Volume of the Hemisphere = (2/3) × π × (Radius)^3

Substituting the given radius of 2.1 cm into the formula, we can calculate the volume of the hemisphere:

Volume of the Hemisphere = (2/3) × π × (2.1 cm)^3 ≈ (2/3) × 3.14 × 9.261 cm^3 ≈ 19.48 cm^3

Total Volume of the Block:
To find the total volume of the block, we add the volume of the cube and the volume of the hemisphere:

Total Volume of the Block = Volume of the Cube + Volume of the Hemisphere
= 216 cm^3 + 19.48 cm^3