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 35 x 15
= 1050 cm2
2 painted areas breadthwise
= 2 x 19 x 15
= 570 cm
2
Base painted area
= 35 x 19
= 665 cm2
Painted areas
= 1050 + 570 + 665
= 2285 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 35 x 19 x 15
= 9975 cm
3 Number of 1-cm cubes in the box when full
= 9975 ÷ 1
= 9975
(c)
Number of cubes that touch the base of the box
= 35 x 19
= 665
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 35 x (15 - 1)
= 2 x 35 x 14
= 980
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (19 - 2) x (15 - 1)
= 2 x 17 x 14
= 476
Number of cubes that touch the inside of the box
= 665 + 980 + 476
= 2121
Answer(s): (a) 2285 cm
2; (b) 9975; (c) 2121