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 15
= 1350 cm2
2 painted areas breadthwise
= 2 x 21 x 15
= 630 cm
2
Base painted area
= 45 x 21
= 945 cm2
Painted areas
= 1350 + 630 + 945
= 2925 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 45 x 21 x 15
= 14175 cm
3 Number of 1-cm cubes in the box when full
= 14175 ÷ 1
= 14175
(c)
Number of cubes that touch the base of the box
= 45 x 21
= 945
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 45 x (15 - 1)
= 2 x 45 x 14
= 1260
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (21 - 2) x (15 - 1)
= 2 x 19 x 14
= 532
Number of cubes that touch the inside of the box
= 945 + 1260 + 532
= 2737
Answer(s): (a) 2925 cm
2; (b) 14175; (c) 2737