PSLE
Riordan had a rectangular block of wood 14 cm by 8 cm by 5 cm. He painted all the faces of the block.

1. What is the total painted area?
2. Riordan 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
= 14 x 8 x 2
= 224 cm²

Total surface area of the front and the back
= 14 x 5 x 2
= 140 cm²

Total surface area of the left and right
= 8 x 5 x 2
= 80 cm²

Total painted area
= 224 + 140 + 80
= 444 cm²

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

Length
= 14 - 1 - 1
= 12 cm

Breadth
= 8 - 1 - 1
= 5 cm

Height
= 5 - 1 -1
= 3 cm

Number of cubes without any painted surface
= ^{12 x 5 x 3}_{1 x 1 x 1}
= 180

(c)
Number of cubes with 2 faces painted lengthwise
= 12 x 4
= 48

Number of cubes with 2 faces painted breadthwise
= 5 x 4
= 20

Number of cubes with 2 cubes painted heightwise
= 3 x 4
= 12

Total number of cubes that have 2 painted surfaces
= 48 + 20 + 12
= 80

Answer(s): (a) 444 cm²; (b) 180; (c) 80