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 28 x 40
= 2240 cm2
2 painted areas breadthwise
= 2 x 20 x 40
= 1600 cm
2
Base painted area
= 28 x 20
= 560 cm2
Painted areas
= 2240 + 1600 + 560
= 4400 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 28 x 20 x 40
= 22400 cm
3 Number of 1-cm cubes in the box when full
= 22400 ÷ 1
= 22400
(c)
Number of cubes that touch the base of the box
= 28 x 20
= 560
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (40 - 1) x 28
= 2 x 39 x 28
= 2184
Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (20 - 2) x (40 - 1)
= 2 x 18 x 39
= 1404
Number of cubes that touch the inside of the box
= 560 + 2184 + 1404
= 4148
Answer(s): (a) 4400 cm
2; (b) 22400; (c) 4148