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 39 x 60
= 4680 cm2
2 painted areas breadthwise
= 2 x 35 x 60
= 4200 cm
2
Base painted area
= 39 x 35
= 1365 cm2
Painted areas
= 4680 + 4200 + 1365
= 10245 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 39 x 35 x 60
= 81900 cm
3 Number of 1-cm cubes in the box when full
= 81900 ÷ 1
= 81900
(c)
Number of cubes that touch the base of the box
= 39 x 35
= 1365
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (60 - 1) x 39
= 2 x 59 x 39
= 4602
Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (35 - 2) x (60 - 1)
= 2 x 33 x 59
= 3894
Number of cubes that touch the inside of the box
= 1365 + 4602 + 3894
= 9861
Answer(s): (a) 10245 cm
2; (b) 81900; (c) 9861