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 22 x 45
= 1980 cm2
2 painted areas breadthwise
= 2 x 15 x 45
= 1350 cm
2
Base painted area
= 22 x 15
= 330 cm2
Painted areas
= 1980 + 1350 + 330
= 3660 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 22 x 15 x 45
= 14850 cm
3 Number of 1-cm cubes in the box when full
= 14850 ÷ 1
= 14850
(c)
Number of cubes that touch the base of the box
= 22 x 15
= 330
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (45 - 1) x 22
= 2 x 44 x 22
= 1936
Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (15 - 2) x (45 - 1)
= 2 x 13 x 44
= 1144
Number of cubes that touch the inside of the box
= 330 + 1936 + 1144
= 3410
Answer(s): (a) 3660 cm
2; (b) 14850; (c) 3410