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 60 x 30
= 3600 cm2
2 painted areas breadthwise
= 2 x 36 x 30
= 2160 cm
2
Base painted area
= 60 x 36
= 2160 cm2
Painted areas
= 3600 + 2160 + 2160
= 7920 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 60 x 36 x 30
= 64800 cm
3 Number of 1-cm cubes in the box when full
= 64800 ÷ 1
= 64800
(c)
Number of cubes that touch the base of the box
= 60 x 36
= 2160
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 60 x (30 - 1)
= 2 x 60 x 29
= 3480
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (36 - 2) x (30 - 1)
= 2 x 34 x 29
= 1972
Number of cubes that touch the inside of the box
= 2160 + 3480 + 1972
= 7612
Answer(s): (a) 7920 cm
2; (b) 64800; (c) 7612