PSLE Vaidev had a rectangular block of wood 16 cm by 11 cm by 7 cm. He painted all the faces of the block.
- What is the total painted area?
- Vaidev 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 11 x 2
= 352 cm
2 Total surface area of the front and the back
= 16 x 7 x 2
= 224 cm
2 Total surface area of the left and right
= 11 x 7 x 2
= 154 cm
2 Total painted area
= 352 + 224 + 154
= 730 cm
2 (b)
Dimension of the cuboid that does not have any painted surface.
Length
= 16 - 1 - 1
= 14 cm
Breadth
= 11 - 1 - 1
= 7 cm
Height
= 7 - 1 -1
= 5 cm
Number of cubes without any painted surface
=
14 x 7 x 51 x 1 x 1 = 490
(c)
Number of cubes with 2 faces painted lengthwise
= 14 x 4
= 56
Number of cubes with 2 faces painted breadthwise
= 7 x 4
= 28
Number of cubes with 2 cubes painted heightwise
= 5 x 4
= 20
Total number of cubes that have 2 painted surfaces
= 56 + 28 + 20
= 104
Answer(s): (a) 730 cm
2; (b) 490; (c) 104