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 65 x 40
= 5200 cm2
2 painted areas breadthwise
= 2 x 47 x 40
= 3760 cm
2
Base painted area
= 65 x 47
= 3055 cm2
Painted areas
= 5200 + 3760 + 3055
= 12015 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 65 x 47 x 40
= 122200 cm
3 Number of 1-cm cubes in the box when full
= 122200 ÷ 1
= 122200
(c)
Number of cubes that touch the base of the box
= 65 x 47
= 3055
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 65 x (40 - 1)
= 2 x 65 x 39
= 5070
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (47 - 2) x (40 - 1)
= 2 x 45 x 39
= 3510
Number of cubes that touch the inside of the box
= 3055 + 5070 + 3510
= 11635
Answer(s): (a) 12015 cm
2; (b) 122200; (c) 11635