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 43 x 70
= 6020 cm2
2 painted areas breadthwise
= 2 x 40 x 70
= 5600 cm
2
Base painted area
= 43 x 40
= 1720 cm2
Painted areas
= 6020 + 5600 + 1720
= 13340 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 43 x 40 x 70
= 120400 cm
3 Number of 1-cm cubes in the box when full
= 120400 ÷ 1
= 120400
(c)
Number of cubes that touch the base of the box
= 43 x 40
= 1720
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (70 - 1) x 43
= 2 x 69 x 43
= 5934
Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (40 - 2) x (70 - 1)
= 2 x 38 x 69
= 5244
Number of cubes that touch the inside of the box
= 1720 + 5934 + 5244
= 12898
Answer(s): (a) 13340 cm
2; (b) 120400; (c) 12898