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 38 x 50
= 3800 cm2
2 painted areas breadthwise
= 2 x 30 x 50
= 3000 cm
2
Base painted area
= 38 x 30
= 1140 cm2
Painted areas
= 3800 + 3000 + 1140
= 7940 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 38 x 30 x 50
= 57000 cm
3 Number of 1-cm cubes in the box when full
= 57000 ÷ 1
= 57000
(c)
Number of cubes that touch the base of the box
= 38 x 30
= 1140
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (50 - 1) x 38
= 2 x 49 x 38
= 3724
Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (30 - 2) x (50 - 1)
= 2 x 28 x 49
= 2744
Number of cubes that touch the inside of the box
= 1140 + 3724 + 2744
= 7608
Answer(s): (a) 7940 cm
2; (b) 57000; (c) 7608