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 28 x 50
= 2800 cm2
2 painted areas breadthwise
= 2 x 20 x 50
= 2000 cm
2
Base painted area
= 28 x 20
= 560 cm2
Painted areas
= 2800 + 2000 + 560
= 5360 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 28 x 20 x 50
= 28000 cm
3 Number of 1-cm cubes in the box when full
= 28000 ÷ 1
= 28000
(c)
Number of cubes that touch the base of the box
= 28 x 20
= 560
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (50 - 1) x 28
= 2 x 49 x 28
= 2744
Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (20 - 2) x (50 - 1)
= 2 x 18 x 49
= 1764
Number of cubes that touch the inside of the box
= 560 + 2744 + 1764
= 5068
Answer(s): (a) 5360 cm
2; (b) 28000; (c) 5068