PSLE Julian had a rectangular block of wood 15 cm by 11 cm by 7 cm. He painted all the faces of the block.
- What is the total painted area?
- Julian 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
= 15 x 11 x 2
= 330 cm
2 Total surface area of the front and the back
= 15 x 7 x 2
= 210 cm
2 Total surface area of the left and right
= 11 x 7 x 2
= 154 cm
2 Total painted area
= 330 + 210 + 154
= 694 cm
2 (b)
Dimension of the cuboid that does not have any painted surface.
Length
= 15 - 1 - 1
= 13 cm
Breadth
= 11 - 1 - 1
= 7 cm
Height
= 7 - 1 -1
= 5 cm
Number of cubes without any painted surface
=
13 x 7 x 51 x 1 x 1 = 455
(c)
Number of cubes with 2 faces painted lengthwise
= 13 x 4
= 52
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
= 52 + 28 + 20
= 100
Answer(s): (a) 694 cm
2; (b) 455; (c) 100