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 21 x 40
= 1680 cm2
2 painted areas breadthwise
= 2 x 15 x 40
= 1200 cm
2
Base painted area
= 21 x 15
= 315 cm2
Painted areas
= 1680 + 1200 + 315
= 3195 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 21 x 15 x 40
= 12600 cm
3 Number of 1-cm cubes in the box when full
= 12600 ÷ 1
= 12600
(c)
Number of cubes that touch the base of the box
= 21 x 15
= 315
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (40 - 1) x 21
= 2 x 39 x 21
= 1638
Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (15 - 2) x (40 - 1)
= 2 x 13 x 39
= 1014
Number of cubes that touch the inside of the box
= 315 + 1638 + 1014
= 2967
Answer(s): (a) 3195 cm
2; (b) 12600; (c) 2967