PSLE
Carl had a rectangular block of wood 13 cm by 11 cm by 7 cm. He painted all the faces of the block.

1. What is the total painted area?
2. Carl 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
= 13 x 11 x 2
= 286 cm²

Total surface area of the front and the back
= 13 x 7 x 2
= 182 cm²

Total surface area of the left and right
= 11 x 7 x 2
= 154 cm²

Total painted area
= 286 + 182 + 154
= 622 cm²

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

Length
= 13 - 1 - 1
= 11 cm

Breadth
= 11 - 1 - 1
= 7 cm

Height
= 7 - 1 -1
= 5 cm

Number of cubes without any painted surface
= ^{11 x 7 x 5}_{1 x 1 x 1}
= 385

(c)
Number of cubes with 2 faces painted lengthwise
= 11 x 4
= 44

Number of cubes with 2 faces painted breadthwise
= 7 x 4
= 28

Number of cubes with 2 cubes painted heightwise
= 5 x 4
= 20

Total number of cubes that have 2 painted surfaces
= 44 + 28 + 20
= 92

Answer(s): (a) 622 cm²; (b) 385; (c) 92