PSLE Tom had a rectangular block of wood 16 cm by 12 cm by 10 cm. He painted all the faces of the block.
- What is the total painted area?
- Tom 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
= 16 x 12 x 2
= 384 cm
2 Total surface area of the front and the back
= 16 x 10 x 2
= 320 cm
2 Total surface area of the left and right
= 12 x 10 x 2
= 240 cm
2 Total painted area
= 384 + 320 + 240
= 944 cm
2 (b)
Dimension of the cuboid that does not have any painted surface.
Length
= 16 - 1 - 1
= 14 cm
Breadth
= 12 - 1 - 1
= 10 cm
Height
= 10 - 1 -1
= 8 cm
Number of cubes without any painted surface
=
14 x 10 x 81 x 1 x 1 = 1120
(c)
Number of cubes with 2 faces painted lengthwise
= 14 x 4
= 56
Number of cubes with 2 faces painted breadthwise
= 10 x 4
= 40
Number of cubes with 2 cubes painted heightwise
= 8 x 4
= 32
Total number of cubes that have 2 painted surfaces
= 56 + 40 + 32
= 128
Answer(s): (a) 944 cm
2; (b) 1120; (c) 128