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 46 x 60
= 5520 cm2
2 painted areas breadthwise
= 2 x 40 x 60
= 4800 cm
2
Base painted area
= 46 x 40
= 1840 cm2
Painted areas
= 5520 + 4800 + 1840
= 12160 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 46 x 40 x 60
= 110400 cm
3 Number of 1-cm cubes in the box when full
= 110400 ÷ 1
= 110400
(c)
Number of cubes that touch the base of the box
= 46 x 40
= 1840
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (60 - 1) x 46
= 2 x 59 x 46
= 5428
Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (40 - 2) x (60 - 1)
= 2 x 38 x 59
= 4484
Number of cubes that touch the inside of the box
= 1840 + 5428 + 4484
= 11752
Answer(s): (a) 12160 cm
2; (b) 110400; (c) 11752