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 50 x 30
= 3000 cm2
2 painted areas breadthwise
= 2 x 39 x 30
= 2340 cm
2
Base painted area
= 50 x 39
= 1950 cm2
Painted areas
= 3000 + 2340 + 1950
= 7290 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 50 x 39 x 30
= 58500 cm
3 Number of 1-cm cubes in the box when full
= 58500 ÷ 1
= 58500
(c)
Number of cubes that touch the base of the box
= 50 x 39
= 1950
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 50 x (30 - 1)
= 2 x 50 x 29
= 2900
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (39 - 2) x (30 - 1)
= 2 x 37 x 29
= 2146
Number of cubes that touch the inside of the box
= 1950 + 2900 + 2146
= 6996
Answer(s): (a) 7290 cm
2; (b) 58500; (c) 6996