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 70 x 40
= 5600 cm2
2 painted areas breadthwise
= 2 x 50 x 40
= 4000 cm
2
Base painted area
= 70 x 50
= 3500 cm2
Painted areas
= 5600 + 4000 + 3500
= 13100 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 70 x 50 x 40
= 140000 cm
3 Number of 1-cm cubes in the box when full
= 140000 ÷ 1
= 140000
(c)
Number of cubes that touch the base of the box
= 70 x 50
= 3500
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 70 x (40 - 1)
= 2 x 70 x 39
= 5460
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (50 - 2) x (40 - 1)
= 2 x 48 x 39
= 3744
Number of cubes that touch the inside of the box
= 3500 + 5460 + 3744
= 12704
Answer(s): (a) 13100 cm
2; (b) 140000; (c) 12704