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 45 x 20
= 1800 cm2
2 painted areas breadthwise
= 2 x 30 x 20
= 1200 cm
2
Base painted area
= 45 x 30
= 1350 cm2
Painted areas
= 1800 + 1200 + 1350
= 4350 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 45 x 30 x 20
= 27000 cm
3 Number of 1-cm cubes in the box when full
= 27000 ÷ 1
= 27000
(c)
Number of cubes that touch the base of the box
= 45 x 30
= 1350
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 45 x (20 - 1)
= 2 x 45 x 19
= 1710
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (30 - 2) x (20 - 1)
= 2 x 28 x 19
= 1064
Number of cubes that touch the inside of the box
= 1350 + 1710 + 1064
= 4124
Answer(s): (a) 4350 cm
2; (b) 27000; (c) 4124