PSLE An open rectangular box is shown.
- The inside of the box including the base is painted. Find the painted area.
- When the box is packed full with 1-cm cubes, how many cubes are there?
- How many cubes touch inside the box as a result?
(a)
2 painted areas lengthwise
= 2 x 48 x 60
= 5760 cm2
2 painted areas breadthwise
= 2 x 40 x 60
= 4800 cm
2
Base painted area
= 48 x 40
= 1920 cm2
Painted areas
= 5760 + 4800 + 1920
= 12480 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 48 x 40 x 60
= 115200 cm
3 Number of 1-cm cubes in the box when full
= 115200 ÷ 1
= 115200
(c)
Number of cubes that touch the base of the box
= 48 x 40
= 1920
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (60 - 1) x 48
= 2 x 59 x 48
= 5664
Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (40 - 2) x (60 - 1)
= 2 x 38 x 59
= 4484
Number of cubes that touch the inside of the box
= 1920 + 5664 + 4484
= 12068
Answer(s): (a) 12480 cm
2; (b) 115200; (c) 12068