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 43 x 40
= 3440 cm
2
Base painted area
= 60 x 43
= 2580 cm2
Painted areas
= 4800 + 3440 + 2580
= 10820 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 60 x 43 x 40
= 103200 cm
3 Number of 1-cm cubes in the box when full
= 103200 ÷ 1
= 103200
(c)
Number of cubes that touch the base of the box
= 60 x 43
= 2580
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 (43 - 2) x (40 - 1)
= 2 x 41 x 39
= 3198
Number of cubes that touch the inside of the box
= 2580 + 4680 + 3198
= 10458
Answer(s): (a) 10820 cm
2; (b) 103200; (c) 10458