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 50 x 20
= 2000 cm2
2 painted areas breadthwise
= 2 x 29 x 20
= 1160 cm
2
Base painted area
= 50 x 29
= 1450 cm2
Painted areas
= 2000 + 1160 + 1450
= 4610 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 50 x 29 x 20
= 29000 cm
3 Number of 1-cm cubes in the box when full
= 29000 ÷ 1
= 29000
(c)
Number of cubes that touch the base of the box
= 50 x 29
= 1450
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 50 x (20 - 1)
= 2 x 50 x 19
= 1900
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (29 - 2) x (20 - 1)
= 2 x 27 x 19
= 1026
Number of cubes that touch the inside of the box
= 1450 + 1900 + 1026
= 4376
Answer(s): (a) 4610 cm
2; (b) 29000; (c) 4376