PSLE Ryan had a rectangular block of wood 12 cm by 7 cm by 4 cm. He painted all the faces of the block.
- What is the total painted area?
- Ryan then cut the block into 1-cm cubes. How many of these cubes have none of the faces painted?
- How many of these cubes have 2 of the faces painted?
(a)
Total surface area of the top and the bottom
= 12 x 7 x 2
= 168 cm
2 Total surface area of the front and the back
= 12 x 4 x 2
= 96 cm
2 Total surface area of the left and right
= 7 x 4 x 2
= 56 cm
2 Total painted area
= 168 + 96 + 56
= 320 cm
2 (b)
Dimension of the cuboid that does not have any painted surface.
Length
= 12 - 1 - 1
= 10 cm
Breadth
= 7 - 1 - 1
= 4 cm
Height
= 4 - 1 -1
= 2 cm
Number of cubes without any painted surface
=
10 x 4 x 21 x 1 x 1 = 80
(c)
Number of cubes with 2 faces painted lengthwise
= 10 x 4
= 40
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
= 40 + 16 + 8
= 64
Answer(s): (a) 320 cm
2; (b) 80; (c) 64