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 55 x 30
= 3300 cm2
2 painted areas breadthwise
= 2 x 37 x 30
= 2220 cm
2
Base painted area
= 55 x 37
= 2035 cm2
Painted areas
= 3300 + 2220 + 2035
= 7555 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 55 x 37 x 30
= 61050 cm
3 Number of 1-cm cubes in the box when full
= 61050 ÷ 1
= 61050
(c)
Number of cubes that touch the base of the box
= 55 x 37
= 2035
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 55 x (30 - 1)
= 2 x 55 x 29
= 3190
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (37 - 2) x (30 - 1)
= 2 x 35 x 29
= 2030
Number of cubes that touch the inside of the box
= 2035 + 3190 + 2030
= 7255
Answer(s): (a) 7555 cm
2; (b) 61050; (c) 7255