PSLE Valen had a rectangular block of wood 13 cm by 10 cm by 7 cm. He painted all the faces of the block.
- What is the total painted area?
- Valen 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
= 13 x 10 x 2
= 260 cm
2 Total surface area of the front and the back
= 13 x 7 x 2
= 182 cm
2 Total surface area of the left and right
= 10 x 7 x 2
= 140 cm
2 Total painted area
= 260 + 182 + 140
= 582 cm
2 (b)
Dimension of the cuboid that does not have any painted surface.
Length
= 13 - 1 - 1
= 11 cm
Breadth
= 10 - 1 - 1
= 7 cm
Height
= 7 - 1 -1
= 5 cm
Number of cubes without any painted surface
=
11 x 7 x 51 x 1 x 1 = 385
(c)
Number of cubes with 2 faces painted lengthwise
= 11 x 4
= 44
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
= 44 + 28 + 20
= 92
Answer(s): (a) 582 cm
2; (b) 385; (c) 92