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 45 x 15
= 1350 cm2
2 painted areas breadthwise
= 2 x 24 x 15
= 720 cm
2
Base painted area
= 45 x 24
= 1080 cm2
Painted areas
= 1350 + 720 + 1080
= 3150 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 45 x 24 x 15
= 16200 cm
3 Number of 1-cm cubes in the box when full
= 16200 ÷ 1
= 16200
(c)
Number of cubes that touch the base of the box
= 45 x 24
= 1080
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 45 x (15 - 1)
= 2 x 45 x 14
= 1260
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (24 - 2) x (15 - 1)
= 2 x 22 x 14
= 616
Number of cubes that touch the inside of the box
= 1080 + 1260 + 616
= 2956
Answer(s): (a) 3150 cm
2; (b) 16200; (c) 2956