PSLE
Japheth had a rectangular block of wood 10 cm by 6 cm by 4 cm. He painted all the faces of the block.

1. What is the total painted area?
2. Japheth 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
= 10 x 6 x 2
= 120 cm²

Total surface area of the front and the back
= 10 x 4 x 2
= 80 cm²

Total surface area of the left and right
= 6 x 4 x 2
= 48 cm²

Total painted area
= 120 + 80 + 48
= 248 cm²

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

Length
= 10 - 1 - 1
= 8 cm

Breadth
= 6 - 1 - 1
= 4 cm

Height
= 4 - 1 -1
= 2 cm

Number of cubes without any painted surface
= ^{8 x 4 x 2}_{1 x 1 x 1}
= 64

(c)
Number of cubes with 2 faces painted lengthwise
= 8 x 4
= 32

Number of cubes with 2 faces painted breadthwise
= 4 x 4
= 16

Number of cubes with 2 cubes painted heightwise
= 2 x 4
= 8

Total number of cubes that have 2 painted surfaces
= 32 + 16 + 8
= 56

Answer(s): (a) 248 cm²; (b) 64; (c) 56