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 60 x 30
= 3600 cm2
2 painted areas breadthwise
= 2 x 34 x 30
= 2040 cm
2
Base painted area
= 60 x 34
= 2040 cm2
Painted areas
= 3600 + 2040 + 2040
= 7680 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 60 x 34 x 30
= 61200 cm
3 Number of 1-cm cubes in the box when full
= 61200 ÷ 1
= 61200
(c)
Number of cubes that touch the base of the box
= 60 x 34
= 2040
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 60 x (30 - 1)
= 2 x 60 x 29
= 3480
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (34 - 2) x (30 - 1)
= 2 x 32 x 29
= 1856
Number of cubes that touch the inside of the box
= 2040 + 3480 + 1856
= 7376
Answer(s): (a) 7680 cm
2; (b) 61200; (c) 7376