PSLE
An open rectangular box is shown.

1. The inside of the box including the base is painted. Find the painted area.
2. When the box is packed full with 1-cm cubes, how many cubes are there?
3. How many cubes touch inside the box as a result?

(a)
2 painted areas lengthwise
= 2 x 43 x 55
= 4730 cm2

2 painted areas breadthwise
= 2 x 35 x 55
= 3850 cm²

Base painted area 
= 43 x 35
= 1505 cm2

Painted areas
= 4730 + 3850 + 1505
= 10085 cm²

(b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm³

Volume of the box
= 43 x 35 x 55
= 82775 cm³

Number of 1-cm cubes in the box when full
= 82775 ÷ 1
= 82775

(c)
Number of cubes that touch the base of the box 
= 43 x 35
= 1505

Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (55 - 1) x 43
= 2 x 54 x 43
= 4644

Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (35 - 2) x (55 - 1) 
= 2 x 33 x 54
= 3564

Number of cubes that touch the inside of the box
= 1505 + 4644 + 3564 
= 9713

Answer(s): (a) 10085 cm²; (b) 82775; (c) 9713