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 25
= 2500 cm2
2 painted areas breadthwise
= 2 x 34 x 25
= 1700 cm
2
Base painted area
= 50 x 34
= 1700 cm2
Painted areas
= 2500 + 1700 + 1700
= 5900 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 50 x 34 x 25
= 42500 cm
3 Number of 1-cm cubes in the box when full
= 42500 ÷ 1
= 42500
(c)
Number of cubes that touch the base of the box
= 50 x 34
= 1700
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 50 x (25 - 1)
= 2 x 50 x 24
= 2400
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (34 - 2) x (25 - 1)
= 2 x 32 x 24
= 1536
Number of cubes that touch the inside of the box
= 1700 + 2400 + 1536
= 5636
Answer(s): (a) 5900 cm
2; (b) 42500; (c) 5636