PSLE
Tim had a rectangular block of wood 16 cm by 8 cm by 6 cm. He painted all the faces of the block.

1. What is the total painted area?
2. Tim then cut the block into 1-cm cubes. How many of these cubes have none of the faces painted?
3. How many of these cubes have 2 of the faces painted?

(a)
Total surface area of the top and the bottom
= 16 x 8 x 2
= 256 cm²

Total surface area of the front and the back
= 16 x 6 x 2
= 192 cm²

Total surface area of the left and right
= 8 x 6 x 2
= 96 cm²

Total painted area
= 256 + 192 + 96
= 544 cm²

(b)
Dimension of the cuboid that does not have any painted surface.

Length
= 16 - 1 - 1
= 14 cm

Breadth
= 8 - 1 - 1
= 6 cm

Height
= 6 - 1 -1
= 4 cm

Number of cubes without any painted surface
= ^{14 x 6 x 4}_{1 x 1 x 1}
= 336

(c)
Number of cubes with 2 faces painted lengthwise
= 14 x 4
= 56

Number of cubes with 2 faces painted breadthwise
= 6 x 4
= 24

Number of cubes with 2 cubes painted heightwise
= 4 x 4
= 16

Total number of cubes that have 2 painted surfaces
= 56 + 24 + 16
= 96

Answer(s): (a) 544 cm²; (b) 336; (c) 96