The 3D solid given below has edges of equal length of 16 cm. A rectangular hole of dimensions 4x3 cm and depth 2 cm is made in the centre of each face. Calculate the total surface area of the resulting solid in square cm.
Show Hint
When calculating surface area after removing portions of a solid, subtract the area of the removed parts from the total surface area.
Step 1: Understand the shape and dimensions.
The given solid is a polyhedron with edges of length 16 cm. A rectangular hole of dimensions 4 cm x 3 cm is drilled into the center of each face.
Step 2: Surface area of a polyhedron.
The surface area of a polyhedron with 6 faces, each of side 16 cm, is given by:
\[
\text{Surface Area of a face} = 16^2 = 256 \, \text{cm}^2.
\]
The total surface area of the polyhedron is:
\[
\text{Total Surface Area of the polyhedron} = 6 \times 256 = 1536 \, \text{cm}^2.
\]
Step 3: Subtract the area of the holes.
Each hole has dimensions 4 cm x 3 cm, so the area of one hole is:
\[
\text{Area of one hole} = 4 \times 3 = 12 \, \text{cm}^2.
\]
There are 6 holes, one in the center of each face, so the total area of the holes is:
\[
\text{Total hole area} = 6 \times 12 = 72 \, \text{cm}^2.
\]
Step 4: Calculate the final surface area.
The final surface area is the total surface area of the polyhedron minus the total area of the holes:
\[
\text{Final Surface Area} = 1536 - 72 = 1464 \, \text{cm}^2.
\]
Final Answer:
\[
\boxed{1464 \, \text{cm}^2}
\]
