PSLE Japheth had a rectangular block of wood 15 cm by 9 cm by 6 cm. He painted all the faces of the block.
- What is the total painted area?
- Japheth 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
= 15 x 9 x 2
= 270 cm
2 Total surface area of the front and the back
= 15 x 6 x 2
= 180 cm
2 Total surface area of the left and right
= 9 x 6 x 2
= 108 cm
2 Total painted area
= 270 + 180 + 108
= 558 cm
2 (b)
Dimension of the cuboid that does not have any painted surface.
Length
= 15 - 1 - 1
= 13 cm
Breadth
= 9 - 1 - 1
= 6 cm
Height
= 6 - 1 -1
= 4 cm
Number of cubes without any painted surface
=
13 x 6 x 41 x 1 x 1 = 312
(c)
Number of cubes with 2 faces painted lengthwise
= 13 x 4
= 52
Number of cubes with 2 faces painted breadthwise
= 6 x 4
= 24
Number of cubes with 2 cubes painted heightwise
= 4 x 4
= 16
Total number of cubes that have 2 painted surfaces
= 52 + 24 + 16
= 92
Answer(s): (a) 558 cm
2; (b) 312; (c) 92