PSLE
Vincent had a rectangular block of wood 19 cm by 14 cm by 10 cm. He painted all the faces of the block.

1. What is the total painted area?
2. Vincent 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
= 19 x 14 x 2
= 532 cm²

Total surface area of the front and the back
= 19 x 10 x 2
= 380 cm²

Total surface area of the left and right
= 14 x 10 x 2
= 280 cm²

Total painted area
= 532 + 380 + 280
= 1192 cm²

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

Length
= 19 - 1 - 1
= 17 cm

Breadth
= 14 - 1 - 1
= 10 cm

Height
= 10 - 1 -1
= 8 cm

Number of cubes without any painted surface
= ^{17 x 10 x 8}_{1 x 1 x 1}
= 1360

(c)
Number of cubes with 2 faces painted lengthwise
= 17 x 4
= 68

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
= 68 + 40 + 32
= 140

Answer(s): (a) 1192 cm²; (b) 1360; (c) 140