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 33 x 55
= 3630 cm2
2 painted areas breadthwise
= 2 x 30 x 55
= 3300 cm
2
Base painted area
= 33 x 30
= 990 cm2
Painted areas
= 3630 + 3300 + 990
= 7920 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 33 x 30 x 55
= 54450 cm
3 Number of 1-cm cubes in the box when full
= 54450 ÷ 1
= 54450
(c)
Number of cubes that touch the base of the box
= 33 x 30
= 990
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (55 - 1) x 33
= 2 x 54 x 33
= 3564
Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (30 - 2) x (55 - 1)
= 2 x 28 x 54
= 3024
Number of cubes that touch the inside of the box
= 990 + 3564 + 3024
= 7578
Answer(s): (a) 7920 cm
2; (b) 54450; (c) 7578