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 50 x 65
= 6500 cm2
2 painted areas breadthwise
= 2 x 40 x 65
= 5200 cm
2
Base painted area
= 50 x 40
= 2000 cm2
Painted areas
= 6500 + 5200 + 2000
= 13700 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 50 x 40 x 65
= 130000 cm
3 Number of 1-cm cubes in the box when full
= 130000 ÷ 1
= 130000
(c)
Number of cubes that touch the base of the box
= 50 x 40
= 2000
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (65 - 1) x 50
= 2 x 64 x 50
= 6400
Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (40 - 2) x (65 - 1)
= 2 x 38 x 64
= 4864
Number of cubes that touch the inside of the box
= 2000 + 6400 + 4864
= 13264
Answer(s): (a) 13700 cm
2; (b) 130000; (c) 13264