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 32 x 55
= 3520 cm2
2 painted areas breadthwise
= 2 x 25 x 55
= 2750 cm
2
Base painted area
= 32 x 25
= 800 cm2
Painted areas
= 3520 + 2750 + 800
= 7070 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 32 x 25 x 55
= 44000 cm
3 Number of 1-cm cubes in the box when full
= 44000 ÷ 1
= 44000
(c)
Number of cubes that touch the base of the box
= 32 x 25
= 800
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (55 - 1) x 32
= 2 x 54 x 32
= 3456
Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (25 - 2) x (55 - 1)
= 2 x 23 x 54
= 2484
Number of cubes that touch the inside of the box
= 800 + 3456 + 2484
= 6740
Answer(s): (a) 7070 cm
2; (b) 44000; (c) 6740