In the figure given below, a decorative block is shown which is made of two solids, a cube and a hemisphere. The base of the block is a cube with an edge of 6cm and the hemisphere fixed on the top has a diameter of 4.2cm. Find the total surface area of the block.

# In the figure given below, a decorative block is shown which is made of two solids, a cube and a hemisphere. The base of the block is a cube with an edge of 6cm and the hemisphere fixed on the top has a diameter of 4.2cm. Find the total surface area of the block.

1. A

2. B

3. C

4. D

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### 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   where a is the edge of the cube. The formula for the curved surface area of a hemisphere of radius, r is given by   . 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
The curved surface area of the hemisphere is given by  .
We get,

Now, the edge of a cube is 6cm.
The total surface are of a cube of edge a is given by
We get,

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
We get,

The total surface area of the block =
We get,

Thus, the total surface area of the block is   .
Hence, the correct option is 2.

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