PSLE Will had a rectangular block of wood 17 cm by 12 cm by 8 cm. He painted all the faces of the block.
- What is the total painted area?
- Will 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
= 17 x 12 x 2
= 408 cm
2 Total surface area of the front and the back
= 17 x 8 x 2
= 272 cm
2 Total surface area of the left and right
= 12 x 8 x 2
= 192 cm
2 Total painted area
= 408 + 272 + 192
= 872 cm
2 (b)
Dimension of the cuboid that does not have any painted surface.
Length
= 17 - 1 - 1
= 15 cm
Breadth
= 12 - 1 - 1
= 8 cm
Height
= 8 - 1 -1
= 6 cm
Number of cubes without any painted surface
=
15 x 8 x 61 x 1 x 1 = 720
(c)
Number of cubes with 2 faces painted lengthwise
= 15 x 4
= 60
Number of cubes with 2 faces painted breadthwise
= 8 x 4
= 32
Number of cubes with 2 cubes painted heightwise
= 6 x 4
= 24
Total number of cubes that have 2 painted surfaces
= 60 + 32 + 24
= 116
Answer(s): (a) 872 cm
2; (b) 720; (c) 116