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 19 x 15
= 570 cm
2
Base painted area
= 45 x 19
= 855 cm2
Painted areas
= 1350 + 570 + 855
= 2775 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 45 x 19 x 15
= 12825 cm
3 Number of 1-cm cubes in the box when full
= 12825 ÷ 1
= 12825
(c)
Number of cubes that touch the base of the box
= 45 x 19
= 855
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 (19 - 2) x (15 - 1)
= 2 x 17 x 14
= 476
Number of cubes that touch the inside of the box
= 855 + 1260 + 476
= 2591
Answer(s): (a) 2775 cm
2; (b) 12825; (c) 2591