PSLE Fabian had a rectangular block of wood 9 cm by 7 cm by 5 cm. He painted all the faces of the block.
- What is the total painted area?
- Fabian 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
= 9 x 7 x 2
= 126 cm
2 Total surface area of the front and the back
= 9 x 5 x 2
= 90 cm
2 Total surface area of the left and right
= 7 x 5 x 2
= 70 cm
2 Total painted area
= 126 + 90 + 70
= 286 cm
2 (b)
Dimension of the cuboid that does not have any painted surface.
Length
= 9 - 1 - 1
= 7 cm
Breadth
= 7 - 1 - 1
= 5 cm
Height
= 5 - 1 -1
= 3 cm
Number of cubes without any painted surface
=
7 x 5 x 31 x 1 x 1 = 105
(c)
Number of cubes with 2 faces painted lengthwise
= 7 x 4
= 28
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
= 28 + 20 + 12
= 60
Answer(s): (a) 286 cm
2; (b) 105; (c) 60