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 35
= 3850 cm2
2 painted areas breadthwise
= 2 x 44 x 35
= 3080 cm
2
Base painted area
= 55 x 44
= 2420 cm2
Painted areas
= 3850 + 3080 + 2420
= 9350 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 55 x 44 x 35
= 84700 cm
3 Number of 1-cm cubes in the box when full
= 84700 ÷ 1
= 84700
(c)
Number of cubes that touch the base of the box
= 55 x 44
= 2420
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 55 x (35 - 1)
= 2 x 55 x 34
= 3740
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (44 - 2) x (35 - 1)
= 2 x 42 x 34
= 2856
Number of cubes that touch the inside of the box
= 2420 + 3740 + 2856
= 9016
Answer(s): (a) 9350 cm
2; (b) 84700; (c) 9016