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 31 x 50
= 3100 cm2
2 painted areas breadthwise
= 2 x 25 x 50
= 2500 cm
2
Base painted area
= 31 x 25
= 775 cm2
Painted areas
= 3100 + 2500 + 775
= 6375 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 31 x 25 x 50
= 38750 cm
3 Number of 1-cm cubes in the box when full
= 38750 ÷ 1
= 38750
(c)
Number of cubes that touch the base of the box
= 31 x 25
= 775
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (50 - 1) x 31
= 2 x 49 x 31
= 3038
Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (25 - 2) x (50 - 1)
= 2 x 23 x 49
= 2254
Number of cubes that touch the inside of the box
= 775 + 3038 + 2254
= 6067
Answer(s): (a) 6375 cm
2; (b) 38750; (c) 6067