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 50 x 30
= 3000 cm2
2 painted areas breadthwise
= 2 x 35 x 30
= 2100 cm
2
Base painted area
= 50 x 35
= 1750 cm2
Painted areas
= 3000 + 2100 + 1750
= 6850 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 50 x 35 x 30
= 52500 cm
3 Number of 1-cm cubes in the box when full
= 52500 ÷ 1
= 52500
(c)
Number of cubes that touch the base of the box
= 50 x 35
= 1750
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 50 x (30 - 1)
= 2 x 50 x 29
= 2900
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (35 - 2) x (30 - 1)
= 2 x 33 x 29
= 1914
Number of cubes that touch the inside of the box
= 1750 + 2900 + 1914
= 6564
Answer(s): (a) 6850 cm
2; (b) 52500; (c) 6564