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 33 x 45
= 2970 cm2
2 painted areas breadthwise
= 2 x 25 x 45
= 2250 cm
2
Base painted area
= 33 x 25
= 825 cm2
Painted areas
= 2970 + 2250 + 825
= 6045 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 33 x 25 x 45
= 37125 cm
3 Number of 1-cm cubes in the box when full
= 37125 ÷ 1
= 37125
(c)
Number of cubes that touch the base of the box
= 33 x 25
= 825
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (45 - 1) x 33
= 2 x 44 x 33
= 2904
Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (25 - 2) x (45 - 1)
= 2 x 23 x 44
= 2024
Number of cubes that touch the inside of the box
= 825 + 2904 + 2024
= 5753
Answer(s): (a) 6045 cm
2; (b) 37125; (c) 5753