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 45 x 25
= 2250 cm2
2 painted areas breadthwise
= 2 x 32 x 25
= 1600 cm
2
Base painted area
= 45 x 32
= 1440 cm2
Painted areas
= 2250 + 1600 + 1440
= 5290 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 45 x 32 x 25
= 36000 cm
3 Number of 1-cm cubes in the box when full
= 36000 ÷ 1
= 36000
(c)
Number of cubes that touch the base of the box
= 45 x 32
= 1440
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 45 x (25 - 1)
= 2 x 45 x 24
= 2160
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (32 - 2) x (25 - 1)
= 2 x 30 x 24
= 1440
Number of cubes that touch the inside of the box
= 1440 + 2160 + 1440
= 5040
Answer(s): (a) 5290 cm
2; (b) 36000; (c) 5040