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 38 x 60
= 4560 cm2
2 painted areas breadthwise
= 2 x 35 x 60
= 4200 cm
2
Base painted area
= 38 x 35
= 1330 cm2
Painted areas
= 4560 + 4200 + 1330
= 10090 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 38 x 35 x 60
= 79800 cm
3 Number of 1-cm cubes in the box when full
= 79800 ÷ 1
= 79800
(c)
Number of cubes that touch the base of the box
= 38 x 35
= 1330
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (60 - 1) x 38
= 2 x 59 x 38
= 4484
Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (35 - 2) x (60 - 1)
= 2 x 33 x 59
= 3894
Number of cubes that touch the inside of the box
= 1330 + 4484 + 3894
= 9708
Answer(s): (a) 10090 cm
2; (b) 79800; (c) 9708