PSLE Seth had a rectangular block of wood 12 cm by 9 cm by 5 cm. He painted all the faces of the block.
- What is the total painted area?
- Seth 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 9 x 2
= 216 cm
2 Total surface area of the front and the back
= 12 x 5 x 2
= 120 cm
2 Total surface area of the left and right
= 9 x 5 x 2
= 90 cm
2 Total painted area
= 216 + 120 + 90
= 426 cm
2 (b)
Dimension of the cuboid that does not have any painted surface.
Length
= 12 - 1 - 1
= 10 cm
Breadth
= 9 - 1 - 1
= 5 cm
Height
= 5 - 1 -1
= 3 cm
Number of cubes without any painted surface
=
10 x 5 x 31 x 1 x 1 = 150
(c)
Number of cubes with 2 faces painted lengthwise
= 10 x 4
= 40
Number of cubes with 2 faces painted breadthwise
= 5 x 4
= 20
Number of cubes with 2 cubes painted heightwise
= 3 x 4
= 12
Total number of cubes that have 2 painted surfaces
= 40 + 20 + 12
= 72
Answer(s): (a) 426 cm
2; (b) 150; (c) 72