PSLE
John had a rectangular block of wood 16 cm by 13 cm by 10 cm. He painted all the faces of the block.

1. What is the total painted area?
2. John 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 13 x 2
= 416 cm²

Total surface area of the front and the back
= 16 x 10 x 2
= 320 cm²

Total surface area of the left and right
= 13 x 10 x 2
= 260 cm²

Total painted area
= 416 + 320 + 260
= 996 cm²

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

Length
= 16 - 1 - 1
= 14 cm

Breadth
= 13 - 1 - 1
= 10 cm

Height
= 10 - 1 -1
= 8 cm

Number of cubes without any painted surface
= ^{14 x 10 x 8}_{1 x 1 x 1}
= 1120

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

Number of cubes with 2 faces painted breadthwise
= 10 x 4
= 40

Number of cubes with 2 cubes painted heightwise
= 8 x 4
= 32

Total number of cubes that have 2 painted surfaces
= 56 + 40 + 32
= 128

Answer(s): (a) 996 cm²; (b) 1120; (c) 128