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 60 x 40
= 4800 cm2
2 painted areas breadthwise
= 2 x 45 x 40
= 3600 cm
2
Base painted area
= 60 x 45
= 2700 cm2
Painted areas
= 4800 + 3600 + 2700
= 11100 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 60 x 45 x 40
= 108000 cm
3 Number of 1-cm cubes in the box when full
= 108000 ÷ 1
= 108000
(c)
Number of cubes that touch the base of the box
= 60 x 45
= 2700
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 60 x (40 - 1)
= 2 x 60 x 39
= 4680
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (45 - 2) x (40 - 1)
= 2 x 43 x 39
= 3354
Number of cubes that touch the inside of the box
= 2700 + 4680 + 3354
= 10734
Answer(s): (a) 11100 cm
2; (b) 108000; (c) 10734