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 35
= 4200 cm2
2 painted areas breadthwise
= 2 x 40 x 35
= 2800 cm
2
Base painted area
= 60 x 40
= 2400 cm2
Painted areas
= 4200 + 2800 + 2400
= 9400 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 60 x 40 x 35
= 84000 cm
3 Number of 1-cm cubes in the box when full
= 84000 ÷ 1
= 84000
(c)
Number of cubes that touch the base of the box
= 60 x 40
= 2400
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 60 x (35 - 1)
= 2 x 60 x 34
= 4080
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (40 - 2) x (35 - 1)
= 2 x 38 x 34
= 2584
Number of cubes that touch the inside of the box
= 2400 + 4080 + 2584
= 9064
Answer(s): (a) 9400 cm
2; (b) 84000; (c) 9064