PSLE Warren had a rectangular block of wood 14 cm by 6 cm by 4 cm. He painted all the faces of the block.
- What is the total painted area?
- Warren 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
= 14 x 6 x 2
= 168 cm
2 Total surface area of the front and the back
= 14 x 4 x 2
= 112 cm
2 Total surface area of the left and right
= 6 x 4 x 2
= 48 cm
2 Total painted area
= 168 + 112 + 48
= 328 cm
2 (b)
Dimension of the cuboid that does not have any painted surface.
Length
= 14 - 1 - 1
= 12 cm
Breadth
= 6 - 1 - 1
= 4 cm
Height
= 4 - 1 -1
= 2 cm
Number of cubes without any painted surface
=
12 x 4 x 21 x 1 x 1 = 96
(c)
Number of cubes with 2 faces painted lengthwise
= 12 x 4
= 48
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
= 48 + 16 + 8
= 72
Answer(s): (a) 328 cm
2; (b) 96; (c) 72