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 46 x 70
= 6440 cm2
2 painted areas breadthwise
= 2 x 40 x 70
= 5600 cm
2
Base painted area
= 46 x 40
= 1840 cm2
Painted areas
= 6440 + 5600 + 1840
= 13880 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 46 x 40 x 70
= 128800 cm
3 Number of 1-cm cubes in the box when full
= 128800 ÷ 1
= 128800
(c)
Number of cubes that touch the base of the box
= 46 x 40
= 1840
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (70 - 1) x 46
= 2 x 69 x 46
= 6348
Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (40 - 2) x (70 - 1)
= 2 x 38 x 69
= 5244
Number of cubes that touch the inside of the box
= 1840 + 6348 + 5244
= 13432
Answer(s): (a) 13880 cm
2; (b) 128800; (c) 13432