PSLE Dylan had a rectangular block of wood 17 cm by 13 cm by 9 cm. He painted all the faces of the block.
- What is the total painted area?
- Dylan 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
= 17 x 13 x 2
= 442 cm
2 Total surface area of the front and the back
= 17 x 9 x 2
= 306 cm
2 Total surface area of the left and right
= 13 x 9 x 2
= 234 cm
2 Total painted area
= 442 + 306 + 234
= 982 cm
2 (b)
Dimension of the cuboid that does not have any painted surface.
Length
= 17 - 1 - 1
= 15 cm
Breadth
= 13 - 1 - 1
= 9 cm
Height
= 9 - 1 -1
= 7 cm
Number of cubes without any painted surface
=
15 x 9 x 71 x 1 x 1 = 945
(c)
Number of cubes with 2 faces painted lengthwise
= 15 x 4
= 60
Number of cubes with 2 faces painted breadthwise
= 9 x 4
= 36
Number of cubes with 2 cubes painted heightwise
= 7 x 4
= 28
Total number of cubes that have 2 painted surfaces
= 60 + 36 + 28
= 124
Answer(s): (a) 982 cm
2; (b) 945; (c) 124